750 Sentences With "center of mass" | Random Sentence Generator

This is because the star destroyer is simultaneously rotating about the center of mass and moving its center of mass.

The force from the ground is not applied at the center of mass, but notice that if you extend a line from that arrow, it would pass right through the center of mass.

As before, the gravitational force acts at the center of mass.

I will use the center of mass for the ball-spring system.

A larger distance from the center of mass produces a larger torque.

Angular momentum, center of mass, friction, levers, static equilibrium—it's all there.

Whereas for running, our center of mass moves more like a spring.

We humans have a center of mass that's generally right above our bellybuttons.

Most cars have a center of mass that is not in the center.

However, since it's at the center of mass, it doesn't contribute any torque.

"It's actually a simply matter of center of mass and flat bristles," he wrote.

The video explains that while walking, our center of mass swings like an inverted pendulum.

So check it out: The center of mass (COM) follows the parabolic path we expect.

That might not seem very high—but that is the height of your center of mass.

Of course that velocity calculation is just for the center of mass of the binary systems.

This foot-force exerts a torque about her center of mass and makes her rotate forward.

But the more important thing has to do with the broom's shape and center of mass.

That will keep the center of mass for the head-feet system in a parabolic trajectory.

And for some super-nerdy density physics: Can you calculate the center of mass in Thor's hammer?

It will stay upright so long as its center of mass is positioned between its support points.

If you position its center of mass within the footprint of the brush, it can remain upright.

And crucially, the broom's center of mass is low, probably just a few centimeters above the brush.

Yep, once he pushes off the ground, his center of mass actually follows a normal parabolic trajectory.

I can represent these two parts as balls and then find the center of mass between them.

First, she jumps at least 2 meters high—that's the change in height of her center of mass.

Here's what that would look like: Both of the stars are orbiting around a common center of mass.

Because of that, the handle can lean quite a bit without moving the center of mass very much.

If the stars have equal masses, then that center of mass is the actual center of the circular orbit.

But I've also learned how to think about my body in a new way and appreciate its center of mass.

And the key to the handstand is to make sure your center of mass always remains right over your hands.

The objects are rotating around each other's center of mass at 412 kilometers per second, or 921,618 miles per hour.

"All of his movements are balanced, so the center of mass movement only goes straight up and down," says Matthis.

And once you have a single force, you need a single location for that force—that's the center of mass.

That's because of this very massive auto part called the engine, which shifts the center of mass toward the front.

It's where there are two stars close to each other, and they both orbit around a common center of mass.

WIRED writer Rhett Allain explains that the feat is an illusion: Qiang's center of mass follows a normal parabolic trajectory.

The other secret to handstands is subtle actions of hands and fingers, which can help you steer your center of mass.

An object's center of mass is the point at which you can pretend there's a single gravitational force acting on it.

He occasionally stopped a straggler to show the mechanical principles of center of mass ("The key to C. C. Sabathia's success").

The yellow ball is the head, the red ball is the feet, and the white ball represents the center of mass.

"Any time you have a lever, the farther out the center of mass is, the more force is being applied," she said.

For one thing, the molecule's center of mass is shifted away from the two outlying hydrogen atoms to its central oxygen atom.

I also pulled out the location data and plotted the trajectory of the head, feet, and center of mass in the model.

Maybe angular momentum is only conserved because I am calculating it with respect to the center of mass for the ball-spring system.

With a kick, you've got two extra joints between your [point of] contact and your center of mass just below your belly button.

That means you can draw a line from the cable extending through the car and it will pass through the center of mass.

Any two objects in orbit around each other are actually in orbit around an invisible point called the center of mass, or barycenter.

I can also use Tracker to get the change in height (Δy) of his center of mass as he moves up the wall.

The key here is that her center of mass accelerates down, but she can make a part of her (like her foot) stay stationary.

If the force doesn't pass through the center of mass, the force will also exert a torque on the object, causing it to rotate.

Now suppose you push the pencil near the end: Since the force isn't acting at the center of mass, it will create a torque.

What I've done here is trace the movement of three different parts of his body: his head, his feet, and his center of mass.

The gaze of the Western reader, who lives at the bright center of mass culture, is supposed to shine into every darkness on every continent.

Estimate the location of the center of mass and see how much it would move toward the front if you put the engine back in.

Even a two-legged human: When you stand up from your desk, your center of mass is between your feet, so you don't tip over.

In this case, the researchers were interested in the center of mass of the solar system, the point that everything, even the sun's center, travels around.

However, since I did it anyway—here is my plot of the trajectory of the two sets of wheels along with the center of mass (approximate).

Since these two forces are equal in magnitude but opposite in direction, they won't affect the motion of the center of mass for the whole system.

This is the real center of mass, not just an estimate: This isn't an impossible jump after all—at least not for somebody like Xiao Qiang.

If the wagon's center of mass were closer to the ground, the frictional force on the wheels would produce less torque and it would be more stable.

Acrobats practising tightrope walking, also called funambulism, maintain their balance by positioning their center of mass directly over their base of support, a rope or a wire.

If you had the center of mass directly over the back wheel, then the force from the ground would push straight up and again produce zero torque.

So if you're not spinning very much, then that would result in a sphere, because that force is [symmetric] to a point, which is the center of mass.

"The International Linear Collider (ILC) operating at" the lower "250 GeV center-of-mass energy will provide excellent science from precision studies of the Higgs boson," writes ICFA.

But if it's a forward thrusting knee, you're actually coming in a straight line out from what is effectively your center of mass, or at least close enough.

An object's center of mass is the "average weighted position of all of the tiny masses that comprise the object," according to the American Physical Society's website Physics Central.

It places the center of the reference frame at the Solar System's center of mass, and is oriented based on the position of distant bright radio sources called quasars.

"Cops miss," Moskos said, which is why they're tr rained to shoot at a center of mass — the torso — and not at quickly-moving legs in a stressful situation.

The magnitude of the torque depends on two things: (1) how much force you apply and (2) the distance (r) from the center of mass, called the torque arm.

When the truck goes up this ramp, there will be a force (Ff) pushing on the front tires to produce a counterclockwise torque around the truck's center of mass.

To make a pot on a potter's wheel, you must first manipulate your ball of clay so that its center of mass matches the rotational center of the spinning wheel.

Normally the center of mass would be around a person's belly, but it changes as you move your arms and legs up or down, so this is a rough estimate.

The pulsar, which rotates 366 times per second, co-orbits on the interior with one of the white dwarfs; the pair circles a common center of mass every 1.6 Earth days.

Most of that is in the little battery and motor pack stashed at the top of the shorts, near the body's center of mass, helping it feel lighter than it is.

To date, no killer app has extended the promise of VR from a novelty to a sticky experience or utility that reaches beyond enthusiasts to resonate with the consumer center of mass.

Basically, a metal brick with sensors and the ability to change its center of mass to control its spin to hit a precise orientation at a precise height – to 'stick the landing' every time.

I could probably estimate her mass distribution to calculate her center of mass in each frame—but I will instead just plot the vertical motion of a few of her body parts (feet, arms, torso).

The same way we're held to the Earth by gravity, any stuff can be held to any other stuff by gravity, so those things have a center of mass, and they want to move towards [that] mass.

But the center of mass for space and space policy and funding for space-related stuff is in D.C., so it's a great place to have an anchor network of people who want to help founders succeed.

Remember, the only external force acting on the guy once he leaves the ground is gravity, so the center of mass of the head-feet system (also known as a person) has to follow a parabolic trajectory.

" Here's more specific advice from Physics Central on how to use force to control center of mass: "If you start to fall forward, press hard into your fingertips, and your body will oscillate back toward an upright position.

To get in and out you need a foot behind your center of mass to drive in off, and a foot in front of your center of gravity to catch you and rebound you out of range again.

For anyone who doesn't remember high school physics, a concentration of weight at the belly throws off a person's center of mass, which changes the way gravity affects their bodies and makes even just trying to stand upright much more difficult.

It's not like something like a forward knee where it's like a straight connection between your center of mass and point of impact—it's too complicated or difficult a situation to think you can get all of your mass behind it.

Some have suggested that smaller (and, often by extension, younger) skateboarders have an advantage because of a low center of mass, which might make it easier for them to stay on the board or to twist and turn through the air.

While there's a lot to be said for the forward-facing design â€" mostly that particles don't need to be redirected 90 degrees at the end of their journey â€" it has the unfortunate effect of throwing off the vacuum's center of mass.

In the case of pole dancing, you would measure where the center of mass falls with respect to the pole, then multiply the dancer's weight by whatever that radius is to determine how much total weight they actually have to hold up.

When an object falls on Earth, the Earth exerts a gravitational force on the object, pulling the object towards the Earth's center of mass (and the object pulls back, but because it's a lot smaller than the Earth, that pull is almost imperceptible).

He felt that the NASA team based their theories on an assumption of what the thrust measurement should look like on their graphs, and that what they observed might not actually have been thrust but instead added heat energy changing the cone's center of mass.

The bot is able to be slung from the end of a wire to fly through the air, controlling its pose, rotation and center of mass to not only land aerial tricks correctly but to do them on target while holding heroic poses in midair.

Here's a shot of that hanging car: If you use three attachment points (as seen in the photo), the car can still rotate a little bit to have the center of mass in line with the main cable, but it won't swing too much.

"Basically, when a planet has a moon, the planet is of course pulling on the moon gravitationally, but the moon is also pulling on the planet, and they're both actually orbiting their common center of mass—a point in space along the line between the centers of the two objects," explained Teaching.

Excitingly, Heller and Hippke have also outlined a plan for sending the probe to the system's other stars, namely Alpha Centauri B (the binary companion to Alpha Centauri A) and Proxima Centauri (a distant third star located about 0.22 light-years (1.2 trillion miles) from A and B's common center of mass).

If an Earth-like planet was orbiting at a distance of 1.165-1.195 au (which stands for astronomical unit, and is equal to 149.6 million kilometers—the average distance from the center of the Earth to the center of the sun) from the center of mass of the two stars, it would have a pretty comfortable climate, with liquid water and fairly constant temperatures, according to the study.

Plumb line method The experimental determination of the center of mass of a body uses gravity forces on the body and relies on the fact that in the parallel gravity field near the surface of the earth the center of mass is the same as the center of gravity. The center of mass of a body with an axis of symmetry and constant density must lie on this axis. Thus, the center of mass of a circular cylinder of constant density has its center of mass on the axis of the cylinder. In the same way, the center of mass of a spherically symmetric body of constant density is at the center of the sphere.

Additional parameters, such as the fore-to-aft position of the center of mass and the elevation of the center of mass also contribute to the dynamic behavior of a bike.

In physics, relativistic center of mass refers to the mathematical and physical concepts that define the center of mass of a system of particles in relativistic mechanics and relativistic quantum mechanics.

Archimedes only went as far as the integral of x3, which he used to find the center of mass of a hemisphere, and in other work, the center of mass of a parabola.

The GRACE vehicles also have optical corner reflectors to enable laser ranging from ground stations using the Center of Mass Trim Assembly (MTA) which ensures the center of mass is modified throughout the flight accordingly.

Not only does it have a low center of mass, but it also has a specific shape. At equilibrium, the center of mass and the contact point are on the line perpendicular to the ground. When the toy is pushed, its center of mass rises and also shifts away from that line. This produces a righting moment which returns the toy to the equilibrium position.

There are several methods for locating the center of mass of a body.

This method is useful when one wishes to find the location of the centroid or center of mass of an object that is easily divided into elementary shapes, whose centers of mass are easy to find (see List of centroids). Here the center of mass will only be found in the x direction. The same procedure may be followed to locate the center of mass in the y direction. The shape.

The center of mass is an important point on an aircraft, which significantly affects the stability of the aircraft. To ensure the aircraft is stable enough to be safe to fly, the center of mass must fall within specified limits. If the center of mass is ahead of the forward limit, the aircraft will be less maneuverable, possibly to the point of being unable to rotate for takeoff or flare for landing. If the center of mass is behind the aft limit, the aircraft will be more maneuverable, but also less stable, and possibly unstable enough so as to be impossible to fly.

Kepler's First Law states that an orbit is an ellipse with the center of mass as one focus. In the case of a very small mass falling toward a very large mass M, the center of mass is within the larger mass.

The center of mass is moving at speed and both bodies are moving towards it at speed . Because of the symmetry, after the collision both must be moving away from the center of mass at the same speed. Adding the speed of the center of mass to both, we find that the body that was moving is now stopped and the other is moving away at speed . The bodies have exchanged their velocities.

The tetrahedron's center of mass computes as the arithmetic mean of its four vertices, see Centroid.

The center of mass is a useful reference point for calculations in mechanics that involve masses distributed in space, such as the linear and angular momentum of planetary bodies and rigid body dynamics. In orbital mechanics, the equations of motion of planets are formulated as point masses located at the centers of mass. The center of mass frame is an inertial frame in which the center of mass of a system is at rest with respect to the origin of the coordinate system.

In other words, the center of mass is the particle equivalent of a given object for application of Newton's laws of motion. In the case of a single rigid body, the center of mass is fixed in relation to the body, and if the body has uniform density, it will be located at the centroid. The center of mass may be located outside the physical body, as is sometimes the case for hollow or open-shaped objects, such as a horseshoe. In the case of a distribution of separate bodies, such as the planets of the Solar System, the center of mass may not correspond to the position of any individual member of the system.

The center of mass is the unique point at the center of a distribution of mass in space that has the property that the weighted position vectors relative to this point sum to zero. In analogy to statistics, the center of mass is the mean location of a distribution of mass in space.

In general, for any symmetry of a body, its center of mass will be a fixed point of that symmetry.

The concept of "center of mass" in the form of the center of gravity was first introduced by the great ancient Greek physicist, mathematician, and engineer Archimedes of Syracuse. He worked with simplified assumptions about gravity that amount to a uniform field, thus arriving at the mathematical properties of what we now call the center of mass. Archimedes showed that the torque exerted on a lever by weights resting at various points along the lever is the same as what it would be if all of the weights were moved to a single point—their center of mass. In work on floating bodies he demonstrated that the orientation of a floating object is the one that makes its center of mass as low as possible.

Also, above some threshold of this center-of-mass energy of the system of the two photons, matter can be created.

The center of mass of this figure is at a distance of 8.5 units from the left corner of the figure.

A change of reference frame, can, often, simplify calculations of motion. For example, in a collision of two particles, a reference frame can be chosen, where, one particle begins at rest. Another, commonly used reference frame, is the center of mass frame – one that is moving with the center of mass. In this frame, the total momentum is zero.

The pseudo-worldline of the canonical center of mass is always nearer to the center of inertia than the center of energy.

Under Newton's law of universal gravitation, bodies placed at rest in a central configuration will maintain the configuration as they collapse to a collision at their center of mass. Systems of bodies in a two-dimensional central configuration can orbit stably around their center of mass, maintaining their relative positions, with circular orbits around the center of mass or in elliptical orbits with the center of mass at a focus of the ellipse. These are the only possible stable orbits in three-dimensional space in which the system of particles always remains similar to its initial configuration. More generally, any system of particles moving under Newtonian gravitation that all collide at a single point in time and space will approximate a central configuration, in the limit as time tends to the collision time.

Center of mass acceleration is essential in the feedback mechanism as this feedback takes place before any significant displacement data can be determined.

In physics, a center of gravity of a material body is a point that may be used for a summary description of gravitational interactions. In a uniform gravitational field, the center of mass serves as the center of gravity. This is a very good approximation for smaller bodies near the surface of Earth, so there is no practical need to distinguish "center of gravity" from "center of mass" in most applications, such as engineering and medicine. In a non-uniform field, gravitational effects such as potential energy, force, and torque can no longer be calculated using the center of mass alone.

If the total mass and center of mass can be determined for each area, then the center of mass of the whole is the weighted average of the centers. This method can even work for objects with holes, which can be accounted for as negative masses. A direct development of the planimeter known as an integraph, or integerometer, can be used to establish the position of the centroid or center of mass of an irregular two-dimensional shape. This method can be applied to a shape with an irregular, smooth or complex boundary where other methods are too difficult.

If the center of mass frame is defined by both the mass of matter and the mass of the fictitious fluid, and if the fictitious fluid is indestructible—it's neither created or destroyed—then the motion of the center of mass frame remains uniform. But electromagnetic energy can be converted into other forms of energy. So Poincaré assumed that there exists a non-electric energy fluid at each point of space, into which electromagnetic energy can be transformed and which also carries a mass proportional to the energy. In this way, the motion of the center of mass remains uniform.

A dancer will appear to defy the laws of physics when ballon is exhibited effectively. For example, during a grand jeté, the dancer may appear to hover in the air. Physically, the dancer's center of mass follows a ballistic trajectory, as does any projectile, but observers have limited ability to reckon center of mass when a projectile changes its configuration in flight. By raising the arms and legs while ascending and lowering them while descending, the dancer alters the apparent path of the center of mass and, in so doing, seems to observers to be momentarily floating in the air.

It is not, however, optimized for class separability. However, it has been used to quantify the distance between two or more classes by calculating center of mass for each class in principal component space and reporting Euclidean distance between center of mass of two or more classes. The linear discriminant analysis is an alternative which is optimized for class separability.

Lovejoy, C. O. (1988). Evolution of human walking. Scientific American (0036-8733), 259 (5), p. 82. The human body can endure long-distance running through the following attributes: # Bone and muscle structure: unlike quadruped mammals, which have their center of mass in front of the hind legs or limbs, in biped mammals including humans the center of mass lies right above the legs.

In some models the surfaces are not aligned to the direction of flow acting as airbrakes. Typically the center of mass is at 1/81 and the center of area is at 1/2 of the plane lengths. Two methods exist to shift the center of mass to the front. One rolls up the leading edge which then stays unswept.

The danger of heavy cognitive load is seen in the elderly population. Aging can cause declines in the efficiency of working memory which can contribute to higher cognitive load. The relationship between heavy cognitive load and control of center of mass are heavily correlated in the elderly population. As cognitive load increases, the sway in center of mass in elderly individuals increases.

By decomposition, the orbits of two objects of similar mass can be described as Kepler orbits around their common center of mass, their barycenter.

Chapter 1 of Weight and Balance Handbook (FAA-H-8083-1B), an FAA manual used to show how loading an aircraft changes center of mass.

A pair of translation thrusters are located at the rear of the Soyuz spacecraft; the counter-acting thrusters are similarly paired in the middle of the spacecraft (near the center of mass) pointing outwards and forward. These act in pairs to prevent the spacecraft from rotating. The thrusters for the lateral directions are mounted close to the center of mass of the spacecraft, in pairs as well.

In theropods, the head and neck are greatly pneumatized, and the forearms are reduced. This would help reduce the mass further away from the center of balance. This adjustment to the center of mass would allow the animal to reduce its rotational inertia, thereby increasing its agility. The sacral pneumaticity would lower its center of mass to a more ventral position, allowing it more stabilization.

PLUTO was the first electromagnetic superconductive solenoid in the world, with a very uniform axial magnetic field of 12000 Gauss,Such magnets were later used for Nuclear Magnetic Resonance (NMR) spectroscopy for medical analysis to operate in a straight section of e+e− accelerators at DESY, first with DORIS I (a storage ring at center of mass energies of ~3-5 GeV) in 1974-1976, then with DORIS II (the upgraded storage ring of DORIS I at center of mass energies of ~7-10 Gev) in 1978 and later with PETRA (also a storage ring, at larger center of mass energies of ~10-45 GeV) in 1978-1982 (see review ).

In kinesiology and biomechanics, the center of mass is an important parameter that assists people in understanding their human locomotion. Typically, a human's center of mass is detected with one of two methods: The reaction board method is a static analysis that involves the person lying down on that instrument, and use of their static equilibrium equation to find their center of mass; the segmentation method relies on a mathematical solution based on the physical principle that the summation of the torques of individual body sections, relative to a specified axis, must equal the torque of the whole system that constitutes the body, measured relative to the same axis.

This toy uses the principles of center of mass to keep balance on a finger In physics, the center of mass of a distribution of mass in space (sometimes referred to as the balance point) is the unique point where the weighted relative position of the distributed mass sums to zero. This is the point to which a force may be applied to cause a linear acceleration without an angular acceleration. Calculations in mechanics are often simplified when formulated with respect to the center of mass. It is a hypothetical point where the entire mass of an object may be assumed to be concentrated to visualise its motion.

The most important of details include: mass, center of mass, moment of inertia, thruster positions, thrust vectors, thrust curves, specific impulse, thrust centroid offsets, and fuel consumption.

The weight of the aircraft is the common factor that links all aspects of aircraft design such as aerodynamics, structure, and propulsion, all together. An aircraft's weight is derived from various factors such as empty weight, payload, useful load, etc. The various weights are used to then calculate the center of mass of the entire aircraft. The center of mass must fit within the established limits set by the manufacturer.

Center of mass on a massless leg travelling along the trunk trajectory path in inverted pendulum theory. Velocity vectors are shown perpendicular to the ground reaction force at time 1 and time 2. The inverted pendulum theory of gait is a neuromechanical approach to understanding human movement. In the theory, the weight of the body is reduced to a center of mass resting on a massless leg at a single support.

The moment arm of the elevator will also be reduced, which makes it more difficult to recover from a stalled condition. For helicopters in hover, the center of mass is always directly below the rotorhead. In forward flight, the center of mass will move forward to balance the negative pitch torque produced by applying cyclic control to propel the helicopter forward; consequently a cruising helicopter flies "nose-down" in level flight.

As the propellant level in the rocket goes down, the center of mass initially moves downwards before finally moving upwards again as the propellant is depleted. This initial movement reduces stability and can cause water rockets to start tumbling end over end, greatly decreasing the maximum speed and thus the length of glide (time that the rocket is flying under its own momentum). To lower the center of pressure and add stability, fins or other stabilizers can be added which bring the center of drag further back, well behind the center of mass at all times. Stabilizers of any sort are normally placed near the back of the bottle where the center of mass is found.

A simple model which predicts lyotropic phase transitions is the hard-rod model proposed by Lars Onsager. This theory considers the volume excluded from the center-of-mass of one idealized cylinder as it approaches another. Specifically, if the cylinders are oriented parallel to one another, there is very little volume that is excluded from the center-of-mass of the approaching cylinder (it can come quite close to the other cylinder). If, however, the cylinders are at some angle to one another, then there is a large volume surrounding the cylinder which the approaching cylinder's center-of-mass cannot enter (due to the hard-rod repulsion between the two idealized objects).

Many arboreal species lower their center of mass to reduce pitching and toppling movement when climbing. This may be accomplished by postural changes, altered body proportions, or smaller size.

A general expression for the shape of the path of the TDR convex hulls center of mass has yet to be derived. In order to maintain a smooth rolling motion the center of mass of a rolling body must maintain a constant height. All prime polysphericons, polycons, and platonicons and some of the TDR convex hulls share this property. Some of the TDR convex hulls, like the oloid, do not possess this property.

Albeit, recent studies have depicted that, the first three determinants might actually contribute marginally or far less to reducing the vertical displacement of the center of mass (COM). These determinants of gait are known to ensure economical locomotion,Kuo, A. D., & Donelan, J. M. (2010). Dynamic principles of gait and their clinical implications. Physical therapy, 90(2), 157 by the reduction in vertical center of mass (COM) excursion leading to reduction in metabolic energy.

This article mainly considers symmetric mass distributions, with constant density throughout the object, and the axis of rotation is taken to be through the center of mass unless otherwise specified.

If we think of the numbers in the magic square as masses located in various cells, then the center of mass of a magic square coincides with its geometric center.

The layer of an ecosphere that exists as a gas. The atmosphere is the most distant component sphere of matter from the planet's Center of mass, beyond which is Outer space.

This mass decrease is also equivalent to the energy required to break up the nucleus into individual protons and neutrons. For an isolated system of particles moving in different directions, the invariant mass of the system is the analog of the rest mass, and is the same for all observers, even those in relative motion. It is defined as the total energy (divided by ) in the center of momentum frame. The center of momentum frame is defined so that the system has zero total momentum; the term center of mass frame is also sometimes used, where the center of mass frame is a special case of the center of momentum frame where the center of mass is put at the origin.

When a roly-poly toy is pushed, the height of the center of mass rises from the green line to the orange line, and the center of mass is no longer over the point of contact with the ground. In geometry, a body with a single stable resting position is called monostatic, and the term mono- monostatic has been coined to describe a body which additionally has only one unstable point of balance. (The previously known monostatic polyhedron does not qualify, as it has three unstable equilibria.) A sphere weighted so that its center of mass is shifted from the geometrical center is a mono-monostatic body. A more common example is the Comeback Kid, Weeble or roly-poly toy (see left figure).

Engineers try to design a sports car so that its center of mass is lowered to make the car handle better, that is maintaining traction while executing relatively sharp turns. The characteristic low profile of the U. S. military Humvee was designed in part to allow it tilt farther than taller vehicles, without a rollover, because its low center of mass would stay over the space bounded the four wheels even at angles far from the horizontal.

It is thus said to be a solution of a special case of the two-body problem, known as the Kepler problem. As a theory in classical mechanics, it also does not take into account the effects of general relativity. Keplerian orbits can be parametrized into six orbital elements in various ways. In most applications, there is a large central body, the center of mass of which is assumed to be the center of mass of the entire system.

One electron ion collider in the past was HERA in Hamburg, Germany. Hera ran from 1992 to 2007 and collided electrons and protons at a center of mass energy of 318 GeV.

The layer of an ecosphere that exists at a Terrestrial planet's Center of mass and which extends radially outward until ending in a solid and spherical layer known as the Crust (geology).

The center of mass of a conic solid of uniform density lies one-quarter of the way from the center of the base to the vertex, on the straight line joining the two.

An experimental method for locating the center of mass is to suspend the object from two locations and to drop plumb lines from the suspension points. The intersection of the two lines is the center of mass. The shape of an object might already be mathematically determined, but it may be too complex to use a known formula. In this case, one can subdivide the complex shape into simpler, more elementary shapes, whose centers of mass are easy to find.

For a rigid body, for instance a wheel or an asteroid, the orientation of rotation is simply the position of the rotation axis versus the matter of the body. It may or may not pass through the center of mass, or it may lie completely outside of the body. For the same body, angular momentum may take a different value for every possible axis about which rotation may take place. It reaches a minimum when the axis passes through the center of mass.

The theorem can be generalized to higher-dimensional simplexes using barycentric coordinates. Define a cevian of an n-simplex as a ray from each vertex to a point on the opposite (n-1)-face (facet). Then the cevians are concurrent if and only if a mass distribution can be assigned to the vertices such that each cevian intersects the opposite facet at its center of mass. Moreover, the intersection point of the cevians is the center of mass of the simplex.

Möbius's original formulation of homogeneous coordinates specified the position of a point as the center of mass (or barycenter) of a system of three point masses placed at the vertices of a fixed triangle. Points within the triangle are represented by positive masses and points outside the triangle are represented by allowing negative masses. Multiplying the masses in the system by a scalar does not affect the center of mass, so this is a special case of a system of homogeneous coordinates.

To calculate the net force on a particular body, the nodes of the tree are traversed, starting from the root. If the center of mass of an internal node is sufficiently far from the body, the bodies contained in that part of the tree are treated as a single particle whose position and mass is respectively the center of mass and total mass of the internal node. If the internal node is sufficiently close to the body, the process is repeated for each of its children. Whether a node is or isn't sufficiently far away from a body, depends on the quotient s/d, where s is the width of the region represented by the internal node, and d is the distance between the body and the node's center of mass.

Many families of lizards, including Agamidae, Teiidae, Crotaphytidae, Iguanidae and Phrynosomatidae, have been observed to engage in facultative bipedalism. In lizards, rapid acceleration of the hind legs induces a friction force with the ground, which produces a ground reaction force on the rear legs. When the hind limbs reach the necessary force threshold, the lizard's trunk angle opens and shifts its center of mass; this, in turn, increases front limb elevation, allowing bipedal locomotion over short distances. When modeled, an exact number of steps and rate of acceleration leads to an exact shift in the center of mass that allows the elevation of the front limbs: too fast and the center of mass moves too far back and the lizard falls over backward, too slow and the front limbs never elevate.

The existence of the TMS and the self- stability it exhibits suggests that the design envelope of rideable bikes is larger than previously thought. For example, rear-wheel steering may not be as impossible as has been claimed. In the case of the TMS bike, the authors explain that the front assembly center of mass is lower than the rear frame center of mass – so it falls faster in a lean; and it is in front of the steering axis so it tends to steer the front end in the direction of the lean. They conclude: > As a rule we have found that almost any selfstable bicycle can be made > unstable by mis-adjusting only the trail, or only the front-wheel gyro, or > only the front-assembly center-of-mass position.

The Coulomb barrier causes the cross section to have a strong exponential dependence on the center-of-mass energy . The S-factor remedies this by factoring out the Coulomb component of the cross section.

The Hachitama Spherical Observation Room, located on the 25th floor, provides a view of Tokyo Metropolis. The sphere weighs 1,350 tons and has an off-center of center of mass, which made its installation difficult.

For the case where the masses of two bodies are comparable, an exact Newtonian solution is still sufficient and can be had by placing the coordinate system at the center of mass of the system.

The ground reaction force travels from the center of pressure at the bottom of the massless leg to the center of mass at the top of the massless leg. The velocity vector of the center of mass is always perpendicular to the ground reaction force. Walking consists of alternating single-support and double- support phases. The single-support phase occurs when one leg is in contact with the ground while the double-support phase occurs when two legs are in contact with the ground.

One can further define a unique center of gravity by approximating the field as either parallel or spherically symmetric. The concept of a center of gravity as distinct from the center of mass is rarely used in applications, even in celestial mechanics, where non-uniform fields are important. Since the center of gravity depends on the external field, its motion is harder to determine than the motion of the center of mass. The common method to deal with gravitational torques is a field theory.

The combined center of mass does move slightly to the left when the rider leans to the right relative to the bike, and the bike leans to the left in response. The action, in space, would have the tires move right, but this is prevented by friction between the tires and the ground, and thus pushes the combined center of mass left. This is a small effect, however, as evidenced by the difficulty most people have in balancing a bike by this method alone.

Elastic scattering is a form of particle scattering in scattering theory, nuclear physics and particle physics. In this process, the kinetic energy of a particle is conserved in the center-of-mass frame, but its direction of propagation is modified (by interaction with other particles and/or potentials). Furthermore, while the particle's kinetic energy in the center- of-mass frame is constant, its energy in the lab frame is not. Generally, elastic scattering describes a process in which the total kinetic energy of the system is conserved.

Trailer stability can be defined as the tendency of a trailer to dissipate side-to-side motion. The initial motion may be caused by aerodynamic forces, such as from a cross wind or a passing vehicle. One common criterion for stability is the center of mass location with respect to the wheels, which can usually be detected by tongue weight. If the center of mass of the trailer is behind its wheels, therefore having a negative tongue weight, the trailer will likely be unstable.

Moving along a narrow surface poses special difficulties to animals. During locomotion on the ground, the location of the center of mass may swing from side to side, but during arboreal locomotion, this would result in the center of mass moving beyond the edge of the branch, resulting in a tendency to topple over. Additionally, foot placement is constrained by the need to make contact with the narrow branch. This narrowness severely restricts the range of movements and postures an animal can use to move.

When only one foot is in contact with the ground (known as single limb stance), the center of mass is in front of that foot and moving towards the leg that is in the swing phase.

The center of mass of a typical car is low and slightly ahead of the rear axle, which helps the car track straight as well as providing a slight advantage due to the additional gravitational potential energy.

"Renaissance in Sicht". Physik Journal 12 (8/9): 61-66 (in German).O. Brüning, M. Klein: Preparations for a future Proton-Lepton-collider in the TeV center of mass system , CERN, internal report; called 2013, 17 Sept.

For a mass equal to a Saturn V rocket, the escape velocity relative to the launch pad is 253.5 am/s (8 nanometers per year) faster than the escape velocity relative to the mutual center of mass.

D'Alembert showed that one can transform an accelerating rigid body into an equivalent static system by adding the so-called "inertial force" and "inertial torque" or moment. The inertial force must act through the center of mass and the inertial torque can act anywhere. The system can then be analyzed exactly as a static system subjected to this "inertial force and moment" and the external forces. The advantage is that, in the equivalent static system one can take moments about any point (not just the center of mass).

Although longitudinally stable when stationary, bikes often have a high enough center of mass and a short enough wheelbase to lift a wheel off the ground under sufficient acceleration or deceleration. When braking, depending on the location of the combined center of mass of the bike and rider with respect to the point where the front wheel contacts the ground, bikes can either skid the front wheel or flip the bike and rider over the front wheel. A similar situation is possible while accelerating, but with respect to the rear wheel.

A mature walking pattern is characterized by approximately 60% of the gait cycle (i.e. from one initial contact of a foot to the next initial contact of the same foot) being the stance phase of gait 40% swing phase. Initiation of gait is a voluntary process that involves a preparatory postural adjustment where the center of mass is moved forward and laterally prior to unweighting one leg. The center of mass is only within a person's base of support when both feet are in contact with the ground (known as double limb stance).

Leaning forward places a runner's center of mass on the front part of the foot, which avoids landing on the heel and facilitates the use of the spring mechanism of the foot. It also makes it easier for the runner to avoid landing the foot in front of the center of mass and the resultant braking effect. While upright posture is essential, a runner should maintain a relaxed frame and use their core to keep posture upright and stable. This helps prevent injury as long as the body is neither rigid nor tense.

Center of mass on a massless leg travelling along the trunk trajectory path in inverted pendulum theory. Velocity vectors are shown perpendicular to the ground reaction force at time 1 and time 2. In dynamic walking, the human body can be modeled as the center of mass (COM) supported by a massless rigid leg in single support and two massless legs during double- support,Donelan, J. M., Kram, R., & Kuo, A. D. (2002). Mechanical work for step-to-step transitions is a major determinant of the metabolic cost of human walking.

In all COM frames, the center of mass is at rest, but it is not necessarily at the origin of the coordinate system. In special relativity, the COM frame is necessarily unique only when the system is isolated.

In 2016, Intamin announced an updated version that like Free Spin also features a vehicle with two seating rows rotating independently, and an axis of rotation at the center of mass of each guest to improve rider comfort.

A polytope is called monostatic if, when filled homogeneously, it is stable on only one facet. Alternatively, a polytope is monostatic if its centroid (the center of mass) has an orthogonal projection in the interior of only one facet.

This is why the invariant mass is the same as the rest mass for single particles. However, the invariant mass also represents the measured mass when the center of mass is at rest for systems of many particles. This special frame where this occurs is also called the center of momentum frame, and is defined as the inertial frame in which the center of mass of the object is at rest (another way of stating this is that it is the frame in which the momenta of the system's parts add to zero). For compound objects (made of many smaller objects, some of which may be moving) and sets of unbound objects (some of which may also be moving), only the center of mass of the system is required to be at rest, for the object's relativistic mass to be equal to its rest mass.

The inverted pendulum is stabilized by constant feedback from the brain and can operate even in the presence of sensory loss. In animals who have lost all sensory input to the moving limb, the variables produced by gait (center of mass acceleration, velocity of animal, and position of the animal) remain constant between both groups. During postural control, delayed feedback mechanisms are used in the temporal reproduction of task-level functions such as walking. The nervous system takes into account feedback from the center of mass acceleration, velocity, and position of an individual and utilizes the information to predict and plan future movements.

If a compartment or tank is either empty or full, there is no change in the craft's center of mass as it rolls from side to side (in strong winds, heavy seas, or on sharp motions or turns). However, if the compartment is only partially full, the liquid in the compartment will respond to the vessel's heave, pitch, roll, surge, sway or yaw. For example, as a vessel rolls to port, liquid will displace to the port side of a compartment, and this will move the vessel's center of mass to port. This has the effect of slowing the vessel's return to vertical.

One possible working principle behind a levitation based inertial sensing system is the following. By levitating a micro-object in vacuum and after a cool-down process, the center of mass motion of the micro-object can be controlled and coupled to the kinematic states of the system. Once the system's kinematic state changes (in other words, the system undergoes linear or rotational acceleration), the center of mass motion of the levitated micro-object is affected and yields a signal. This signal is related to the changes of the system's kinematic states and can be read out.

The farther forward (closer to front wheel) the center of mass of the combined bike and rider, the less the front wheel has to move laterally in order to maintain balance. Conversely, the farther back (closer to the rear wheel) the center of mass is located, the more front wheel lateral movement or bike forward motion is required to regain balance. This can be noticeable on long- wheelbase recumbents, choppers, and wheelie bikes. It can also be a challenge for touring bikes that carry a heavy load of gear over or even behind the rear wheel.

X-2 was also able to go "crabwise" with the wheels parallel but out of line with the frame, for instance with the front wheel near the roadway center line and rear wheel near the curb. "Balance" steering allowed easy balancing despite long wheelbase and low center of mass, but no self-balancing ("no hands") configuration was discovered. True circle, as expected, was essentially impossible to balance, as steering does not correct for misalignment of the tire patch and center of mass. Crabwise cycling at angles tested up to about 45° did not show a tendency to fall over, even under braking.

This explanation is contained in The Method. The method that Archimedes describes was based upon his investigations of physics, on the center of mass and the law of the lever. He compared the area or volume of a figure of which he knew the total mass and center of mass with the area or volume of another figure he did not know anything about. He viewed plane figures as made out of infinitely many lines as in the later method of indivisibles, and balanced each line, or slice, of one figure against a corresponding slice of the second figure on a lever.

At heel strike the vertical ground reaction force is located posterior to the axis of rotation of the ankle joint. An external plantar flexion moment is created which must be resisted by an internal dorsiflexion moment. Once the foot is flat and the trunk glides forward over the stance foot, an internal plantar flexion moment is generated to decelerate the forward motion of the body's center of mass. From mid-stance to toe off, however, this moment continues but the function of the plantar flexors switches over to accelerating the knee into extension and propelling the center of mass forward.

A cyclist leaning in a turn A bicycle stays upright while moving forward by being steered so as to keep its center of mass over the wheels. This steering is usually provided by the rider, but under certain conditions may be provided by the bicycle itself. The combined center of mass of a bicycle and its rider must lean into a turn to successfully navigate it. This lean is induced by a method known as countersteering, which can be performed by the rider turning the handlebars directly with the hands or indirectly by leaning the bicycle.

An aerodynamic fairing must be well-shaped, but minimizing the frontal area of the velomobile is also important to reduced drag: a fairing with half the frontal area may approach half the air drag. In turn, aerodynamic velomobiles use a laid-back or recumbent riding position, with the rider's head much lower than on regular bicycles. In turn, velomobile is much easier to accidentally "hide" behind a car or road-side shrubbery, fences, etc. Velomobile bodies are typically light enough that the center of mass is similar to the center of mass on an unfaired recumbent cycle.

Physics of tire imbalance Static balance requires the wheel center of mass to be located on its axis of rotation, usually at the center of the axle on which it is mounted. Static balance can be measured by a static balancing machine where the tire is placed on a vertical, non-rotating spindle. If the center of mass of the tire is not located on this vertical axis, then gravity will cause the axis to deflect. The amount of deflection indicates the magnitude of the unbalance, and the orientation of the deflection indicates the angular location of the unbalance.

The surface of the oloid is a developable surface, meaning that patches of the surface can be flattened into a plane. While rolling, it develops its entire surface: every point of the surface of the oloid touches the plane on which it is rolling, at some point during the rolling movement. Unlike most axial symmetric objects (cylinder, sphere etc.), while rolling on a flat surface, its center of mass performs a meander motion rather than a linear one. In each rolling cycle, the distance between the oloid's center of mass and the rolling surface has two minima and two maxima.

During "flight", the horse's center of mass follows a parabolic trajectory over which it has no control. The horse can change the position of its legs and body in relation to the center of mass, however, which is critical to clearing an obstacle safely. The horse's body rotates through the air, a quality called "bascule", to ensure that while the forehand clears the fence, the shoulders are the highest point of the body, and while the hind end clears the fence, the hips are the highest point of the body. The bascule is the horse's arc over the fence.

A study by Donald Henderson, the curator of dinosaurs at the Royal Tyrrell Museum suggests that Carcharodontosaurus was able to lift animals weighing a maximum of in its jaws based on the strength of its jaws, neck, and its center of mass.

In mechanics, the eigenvectors of the moment of inertia tensor define the principal axes of a rigid body. The tensor of moment of inertia is a key quantity required to determine the rotation of a rigid body around its center of mass.

It was equipped with a powerful petrol engine, it was both wider and larger with a tailored steel chassis, and its center of mass was near the ground. Originally designed as a racing car, the Mercedes was further developed for normal road use.

The most common drive mechanisms of the spherical robots operate by changing the robot's center of mass. Other driving mechanisms make use of: (1) conservation of angular velocity by flywheels, (2) environment's wind, (3) distorting the spherical shell, and (4) gyroscopic effect.

The circumcenter of mass allows an Euler line to be defined for any polygon (and more generally, for a simplicial polytope). This generalized Euler line is defined as the affine span of the center of mass and circumcenter of mass of the polytope.

There is at present a major effort to design and build the International Linear Collider (ILC), which will consist of two opposing linear accelerators, one for electrons and one for positrons. These will collide at a total center of mass energy of 0.5 TeV.

53–54 As in the two-dimensional case, the centroid of the tetrahedron is the center of mass. However contrary to the two-dimensional case the centroid divides the medians not in a 2:1 ratio but in a 3:1 ratio (Commandino's theorem).

The height of all these stances is, ideally, exactly the same, so that the transitions from zenkutsu to kokutsu (defense) or kokutsu to zenkutsu (attack) happen without loss of energy which would be necessary to move the body's center of mass up and down.

Under natural assumptions, the centers of polygons which satisfy Archimedes' Lemma are precisely the points of its Euler line. In other words, the only "well-behaved" centers which satisfy Archimedes' Lemma are the affine combinations of the circumcenter of mass and center of mass.

The significant decrease in the length of the engine compartment allowed the turret to be moved rearwards, which in turn moved its rotation axis and the center of mass"historycy.pl" to the center of the hull, increased the accuracy of the main gun and decreased a chance that the turret could get stuck after getting hit in the turret ring with a projectile that ricocheted. The thickness of the frontal armor protection more than doubled without disturbing the center of mass or drastically increasing the weight of the tank. At the beginning of World War II the thickness of T-34 armor was considered enough.

Consider the problem of estimating the probability that a test point in N-dimensional Euclidean space belongs to a set, where we are given sample points that definitely belong to that set. Our first step would be to find the centroid or center of mass of the sample points. Intuitively, the closer the point in question is to this center of mass, the more likely it is to belong to the set. However, we also need to know if the set is spread out over a large range or a small range, so that we can decide whether a given distance from the center is noteworthy or not.

One area in which these considerations, in some form, become inevitable, is the kinematics of a rigid body. One can take as definition the idea of a curve in the Euclidean group E(3) of three- dimensional Euclidean space, starting at the identity (initial position). The translation subgroup T of E(3) is a normal subgroup, with quotient SO(3) if we look at the subgroup E+(3) of direct isometries only (which is reasonable in kinematics). The translational part can be decoupled from the rotational part in standard Newtonian kinematics by considering the motion of the center of mass, and rotations of the rigid body about the center of mass.

Quantum orbital motion involves the quantum mechanical motion of rigid particles (such as electrons) about some other mass, or about themselves. Typically, orbital motion in classical motion is characterized by orbital angular momentum (the orbital motion of the center of mass) and spin, which is the motion about the center of mass. In quantum mechanics, there are analogous forms of spin and angular momentum, however they differ fundamentally from the models of classical bodies. For example, an electron (one of the main particles of concern in quantum mechanics) exhibits very quantum mechanical behavior in its motion around the nucleus of an atom which cannot be explained by classical mechanics.

In the case of a flowing system of only one chemical constituent, in the Lagrangian representation, there is no distinction between bulk flow and diffusion of matter. Moreover, the flow of matter is zero into or out of the cell that moves with the local center of mass. In effect, in this description, one is dealing with a system effectively closed to the transfer of matter. But still one can validly talk of a distinction between bulk flow and diffusive flow of internal energy, the latter driven by a temperature gradient within the flowing material, and being defined with respect to the local center of mass of the bulk flow.

In astronomy, the barycenter (or barycentre; from the Ancient Greek heavy centerOxford English Dictionary, Second Edition.) is the center of mass of two or more bodies that orbit one another and is the point about which the bodies orbit. It is an important concept in fields such as astronomy and astrophysics. The distance from a body's center of mass to the barycenter can be calculated as a two-body problem. If one of the two orbiting bodies is much more massive than the other and the bodies are relatively close to one another, the barycenter will typically be located within the more massive object.

Mozzi considers a rigid body undergoing first a rotation about an axis passing through the center of mass and then a translation of displacement D in an arbitrary direction. Any rigid motion can be accomplished in this way due to a theorem by Euler on the existence of an axis of rotation. The displacement D of the center of mass can be decomposed into components parallel and perpendicular to the axis. The perpendicular (and parallel) component acts on all points of the rigid body but Mozzi shows that for some points the previous rotation acted exactly with an opposite displacement, so those points are translated parallel to the axis of rotation.

Bug- wipers may be installed to wipe the wings while in flight and remove insects that are disturbing the smooth flow of air over the wing. Modern competition gliders carry jettisonable water ballast (in the wings and sometimes in the vertical stabilizer). The extra weight provided by the water ballast is advantageous if the lift is likely to be strong, and may also be used to adjust the glider's center of mass. Moving the center of mass toward the rear by carrying water in the vertical stabilizer reduces the required down-force from the horizontal stabilizer and the resultant drag from that down-force.

In such systems the origin in the center of mass of the Earth, of the Earth–Moon system, of the Sun, of the Sun plus the major planets, or of the entire Solar System, can be selected.See center-of- mass frame Right ascension and declination are examples of geocentric coordinates, used in Earth-based observations, while the heliocentric latitude and longitude are used for orbital calculations. This leads to such terms as "heliocentric velocity" and "heliocentric angular momentum". In this heliocentric picture, any planet of the Solar System can be used as a source of mechanical energy because it moves relatively to the Sun.

The center of mass lies near the pelvic bone, meaning the creature was bipedal. The forelimbs were shorter than the hindlimbs. The hands had three movable digits while the fourth digit was embedded. It had well-developed claws. The juvenile fossils’ estimated height is from about long.

That is, if the object's center of mass lies over the support polygon, then there exist a set of forces over the region of contact that exactly counteracts the forces of gravity. Note that this is a necessary condition for stability, but not a sufficient one.

The ALICE (A Large Ion Collider Experiment) detector at the LHC at CERN is specialized in studying Pb–Pb nuclei collisions at a center-of-mass energy of 2.76 TeV per nucleon pair. All major LHC detectors—ALICE, ATLAS, CMS and LHCb—participate in the heavy-ion programme.

Duffy, Chris (1979). Siege Warfare: The Fortress in the Early Modern World 1494–1660. Routledge & Kegan Paul. Trunnions were mounted near the center of mass to allow the barrel to be elevated to any desired angle, without having to dismount it from the carriage upon which it rested.

Canadian road sign. The center of mass of a moose is above the hood of most passenger cars. In a collision, the impact crushes the front roof beams and individuals in the front seats. Collisions of this type are frequently fatal; seat belts and airbags offer little protection.

In physics, the center-of-momentum frame (also zero-momentum frame or COM frame) of a system is the unique (up to velocity but not origin) inertial frame in which the total momentum of the system vanishes. The center of momentum of a system is not a location (but a collection of relative momenta/velocities: a reference frame). Thus "center of momentum" means "center-of-momentum frame" and is a short form of this phrase.Dynamics and Relativity, J.R. Forshaw, A.G. Smith, Wiley, 2009, A special case of the center-of-momentum frame is the center-of-mass frame: an inertial frame in which the center of mass (which is a physical point) remains at the origin.

Hubble images of Patroclus and Menoetius orbiting each other, from May to June 2017 Artist's conception of Patroclus and Menoetius orbiting around their center of mass, occasionally eclipsing one another Artist's impression of the Patroclus-Menoetius binary system In 2001, it was discovered that Patroclus is a binary system, made up of two components with of roughly similar size. It is one of 18 binary Trojan asteroids known to exist. In 2006, accurate measurements of the orbit from the Keck Laser guide star adaptive optics system were reported. It was estimated that the two components orbit around their center of mass in days at a distance of in a roughly circular orbit.

A wooden roly-poly toy A roly-poly toy, round-bottomed doll, tilting doll, tumbler or wobbly man is a round-bottomed toy, usually egg-shaped, that tends to right itself when pushed at an angle, and does this in seeming contradiction to how it should fall. The toy is typically hollow with a weight inside the bottom hemisphere. The placement of this weight is such that the toy has a center of mass below the center of the hemisphere, so that any tilting raises the center of mass. When such a toy is pushed over, it wobbles for a few moments while it seeks the upright orientation, which has an equilibrium at the minimum gravitational potential energy.

A line similar to the one described above to analyze braking performance can be drawn from the rear wheel contact patch to predict if a wheelie is possible given the available friction, the center of mass location, and sufficient power. This can also happen on bicycles, although there is much less power available, if the center of mass is back or up far enough or the rider lurches back when applying power to the pedals. Of course, the angle of the terrain can influence all of the calculations above. All else remaining equal, the risk of pitching over the front end is reduced when riding up hill and increased when riding down hill.

Einstein (1906) showed that the inertia of energy (mass-energy- equivalence) is a necessary and sufficient condition for the conservation of the center of mass theorem. On that occasion, he noted that the formal mathematical content of Poincaré paper on the center of mass (1900b) and his own paper were mainly the same, although the physical interpretation was different in light of relativity. Kurd von Mosengeil (1906) by extending Hasenöhrl's calculation of black-body-radiation in a cavity, derived the same expression for the additional mass of a body due to electromagnetic radiation as Hasenöhrl. Hasenöhrl's idea was that the mass of bodies included a contribution from the electromagnetic field, he imagined a body as a cavity containing light.

Now, if the center of mass frame (COM-frame) is defined by both the mass of matter and the mass of the fictitious fluid, and if the fictitious fluid is indestructible – it is neither created or destroyed – then the motion of the center of mass frame remains uniform. But this electromagnetic fluid is not indestructible, because it can be absorbed by matter (which according to Poincaré was the reason why he regarded the em-fluid as "fictitious" rather than "real"). Thus the COM-principle would be violated again. As it was later done by Einstein, an easy solution of this would be to assume that the mass of em-field is transferred to matter in the absorption process.

The SAE's definition of the force based roll center is, "The point in the transverse vertical plane through any pair of wheel centers at which lateral forces may be applied to the sprung mass without producing suspension roll". The lateral location of the roll center is typically at the center-line of the vehicle when the suspension on the left and right sides of the car are mirror images of each other. The significance of the roll center can only be appreciated when the vehicle's center of mass is also considered. If there is a difference between the position of the center of mass and the roll center a moment arm is created.

Important formulas in kinematics define the velocity and acceleration of points in a moving body as they trace trajectories in three-dimensional space. This is particularly important for the center of mass of a body, which is used to derive equations of motion using either Newton's second law or Lagrange's equations.

Kepler-34 is an eclipsing binary star system in the constellation of Cygnus. Both stars have roughly the same mass as the Sun, therefore both are spectral class G. They are separated by 0.22 AU, and complete an eccentric (e=0.5) orbit around a common center of mass every 27 days.

Determining weight, texture, stiffness, center of mass, coefficient of friction, and thermal conductivity require object interaction and some sort of tactile sensing. Several classes of tactile sensors are used in robots in warfare and engineering. Some methods for simultaneous localization and mapping are based on tactile sensors.Fox, Charles, et al.

Wheelies are a common stunt in artistic cycling and freestyle BMX. The bike is balanced by the rider's weight and sometimes use of the rear brake. A style of bicycle, the wheelie bike, has a seating position, and thus center of mass, nearly over the rear wheel that facilitates performing wheelies.

Arboreal species have behaviors specialized for moving in their habitats, most prominently in terms of posture and gait. Specifically, arboreal mammals take longer steps, extend their limbs further forwards and backwards during a step, adopt a more 'crouched' posture to lower their center of mass, and use a diagonal sequence gait.

Due to this the wings may have had a center of mass too close to the wing base for autogyration, or spinning. This led Wolfe and Tanai to suggest that the fruits may have been dispersed by animals and would have fallen straight to the ground, rather than spinning in the wind.

This is a method of determining the center of mass of an L-shaped object. CG of L-shaped object #Divide the shape into two rectangles, as shown in fig 2. Find the center of masses of these two rectangles by drawing the diagonals. Draw a line joining the centers of mass.

The Pauli-Lubanski spin vector is defined to be in the system's rest frame, with the angular-momentum three- vector about the center of mass. In the motion from initial to final position, undergoes a rotation, as recorded in , from its initial to its final value. This continuous change is the Thomas precession.

The forelimbs are smaller and more gracile than the hindlimbs, suggesting that the center of mass for Tanystropheus was closer towards the pelvic girdle. Attachment sites for the m. caudofemoralis muscle complex, coupled with soft- tissue preservation of relative muscle size, further support the proposition that Tanystropheus was a fairly bottom-heavy animal.

In a two-body rotation, such as a planet and moon rotating about their common center of mass or barycentre, the forces on both bodies are centripetal. In that case, the reaction to the centripetal force of the planet on the moon is the centripetal force of the moon on the planet.

By plugging this into the normal distribution we can derive the probability of the test point belonging to the set. The drawback of the above approach was that we assumed that the sample points are distributed about the center of mass in a spherical manner. Were the distribution to be decidedly non-spherical, for instance ellipsoidal, then we would expect the probability of the test point belonging to the set to depend not only on the distance from the center of mass, but also on the direction. In those directions where the ellipsoid has a short axis the test point must be closer, while in those where the axis is long the test point can be further away from the center.

One implementation of two-wheel steering, the Sideways bike, lets the rider control the steering of both wheels directly. Another, the Swing Bike, had the second steering axis in front of the seat so that it could also be controlled by the handlebars. Milton W. Raymond built a long low two-wheel steering bicycle, called "X-2", with various steering mechanisms to control the two wheels independently. Steering motions included "balance", in which both wheels move together to steer the tire contacts under the center of mass; and "true circle", in which the wheels steer equally in opposite directions and thus steering the bicycle without substantially changing the lateral position of the tire contacts relative to the center of mass.

A torque caused by a force \scriptstyle \vec F is a vector quantity defined with respect to some reference point: : \vec \tau = \vec r \times \vec F is the torque vector, and : \ \tau = Fk is the amount of torque. The vector \scriptstyle \vec r is the position vector of the force application point, and in this example it is drawn from the center of mass as the reference point of (see diagram). The straight line segment \scriptstyle k is the lever arm of the force \scriptstyle \vec F with respect to the center of mass. As the illustration suggests, the torque does not change (the same lever arm) if the application point is moved along the line of the application of the force (dotted black line).

The essential point is that the two figures are oriented differently, so that the corresponding slices are at different distances from the fulcrum, and the condition that the slices balance is not the same as the condition that the figures are equal. Once he shows that each slice of one figure balances each slice of the other figure, he concludes that the two figures balance each other. But the center of mass of one figure is known, and the total mass can be placed at this center and it still balances. The second figure has an unknown mass, but the position of its center of mass might be restricted to lie at a certain distance from the fulcrum by a geometrical argument, by symmetry.

Putting the secondary, which is heavier than the primary, in the wider part of the cone allows it to be larger, but it also moves the center of mass aft, potentially causing aerodynamic stability problems during reentry. Dead-weight ballast must be added to the nose to move the center of mass forward. To make the primary small enough to fit into the narrow part of the cone, its bulky insensitive high explosive charges must be replaced with more compact "non-insensitive" high explosives that are more hazardous to handle. The higher yield of the W88, which is the last new warhead produced by the United States, thus comes at a price of higher warhead weight and higher workplace hazard.

Often when a star is a member of a pair of close-orbiting binary stars, the tidal attraction of the gasses near the center of mass are sufficient to pull gas from one star onto its partner. This effect is especially prominent when the partner is a white dwarf, neutron star, or black hole.

A series of propositions of geometry are proved in the palimpsest by similar arguments. One theorem is that the location of a center of mass of a hemisphere is located 5/8 of the way from the pole to the center of the sphere. This problem is notable, because it is evaluating a cubic integral.

Putting this on a mathematical basis, the ellipsoid that best represents the set's probability distribution can be estimated by building the covariance matrix of the samples. The Mahalanobis distance is the distance of the test point from the center of mass divided by the width of the ellipsoid in the direction of the test point.

Historically, the role of the ankle in locomotion has been discussed by Aristotle and Leonardo da Vinci. There is no question that ankle push-off is a significant force in human gait, but how much energy is used in leg swing as opposed to advancing the whole-body center of mass is not clear.

PEP (Positron-Electron Project) began operation in 1980, with center-of-mass energies up to 29 GeV. At its apex, PEP had five large particle detectors in operation, as well as a sixth smaller detector. About 300 researchers made used of PEP. PEP stopped operating in 1990, and PEP-II began construction in 1994.

RX Andromedae is a cataclysmic variable system, where a white dwarf with a mass of 0.8 and an M2 main sequence star are rotating around their center of mass. The main sequence star is overfilling its Roche lobe, so the white dwarf is stripping away matter from the companion star and accreting it through an accretion disk.

Effects of a blow on a hanging beam. CP is the Center of Percussion, and CM is the Center of Mass of the beam. Imagine a rigid beam suspended from a wire by a fixture that can slide freely along the wire at point P, as shown in the Figure. An impulsive blow is applied from the left.

Two stars of different size orbiting the center of mass. The spectrum can be seen to split depending on the position and velocity of the stars. Just as planets can be gravitationally bound to stars, pairs of stars can orbit each other. Some binary stars are visual binaries, meaning they can be observed orbiting each other through a telescope.

Balancing cart, a simple robotics system circa 1976. The cart contains a servo system which monitors the angle of the rod and moves the cart back and forth to keep it upright. An inverted pendulum is a pendulum that has its center of mass above its pivot point. It is unstable and without additional help will fall over.

Stone knapping with limited digital dexterity makes the center of mass the required direction of flake removal. Physics then dictates a circular or oval end pattern, similar to the handaxe, for a leftover core after flake production. This would explain the abundance, wide distribution, proximity to source, consistent shape, and lack of actual use, of these artifacts.

In 1986 the first proton antiproton collisions were recorded at a center of mass energy of 1.8 TeV, making it the highest energy collider in the world, at the time. The most high-energetic collider in the world (as of 2016) is the Large Hadron Collider (LHC) at CERN. There are several particle collider projects currently under consideration.

Kepler-35 is a binary star system in the constellation of Cygnus. These stars, called Kepler-35A and Kepler-35B have masses of 89% and 81% solar masses respectively, and both are assumed to be of spectral class G. They are separated by 0.176 AU, and complete an eccentric orbit around a common center of mass every 20.73 days.

The rolling motion is commonly performed by changing the robot's center of mass (i.e., pendulum- driven system), but there exist some other driving mechanisms . In a wider sense, however, the term "spherical robot" may also be referred to a stationary robot with two rotary joints and one prismatic joint which forms a spherical coordinate system (e.g., Stanford arm ).

The advent of single-molecule studies led in the 2010s to the observation that the movement of untethered enzymes increases with increasing substrate concentration and increasing reaction enthalpy. Subsequent observations suggest that this increase in diffusivity is driven by transient displacement of the enzyme's center of mass, resulting in a "recoil effect that propels the enzyme".

In geometry, a centroidal Voronoi tessellation (CVT) is a special type of Voronoi tessellation or Voronoi diagram. A Voronoi tessellation is called centroidal when the generating point of each Voronoi cell is also its centroid, i.e. the arithmetic mean or center of mass. It can be viewed as an optimal partition corresponding to an optimal distribution of generators.

The ends of the tree experience a tidal force of up to 1/5 g. Each end consists of a leafy "tuft", which is where photosynthesis occurs. Each tuft of a tree is 50 kilometers from the tree's center of mass. Thus, a tuft is either orbiting too slowly (the in tuft) or too quickly (the out tuft).

Another parameter which is less commonly a factor is the trailer moment of inertia. Even if the center of mass is forward of the wheels, a trailer with a long load, and thus large moment of inertia, may be unstable. Some vehicles are equipped with a Trailer Stability Program that may be able to compensate for improper loading.

ADONE (big AdA) was a high-energy (beam energy 1.5 GeV, center-of-mass energy 3 GeV) particle collider. It collided electrons with their antiparticles, positrons. It was 105 meters in circumference. It was operated from 1969 to 1993, by the National Institute of Nuclear Physics (INFN) at the Frascati National Laboratory (LNF), in Frascati, Italy.

Those shifts are very large in comparison to the measurement precisions that are required for astrometry. Thus, the BCRS defines its center of coordinates as the center of mass of the entire Solar System, its barycenter. This stable point for gravity helps to minimize relativistic effects from any observational frames of reference within the Solar System.

The new engine generates and is tilted forwards 55 degrees. It is 43 cm (17 in) wide, giving the bikes a very low center of mass without reducing maximum lean angles.BMW BMW technology site In October 2008, BMW announced the new K1300GT, K1300S and K1300R models, all of which feature a larger capacity 1293 cc engine producing up to .

The term Compact Muon Solenoid comes from the relatively compact size of the detector, the fact that it detects muons, and the use of solenoids in the detector.Aczel, Ammir D. "Present at the Creation: Discovering the Higgs Boson". Random House, 2012 "CMS" is also a reference to the center-of- mass system, an important concept in particle physics.

Similar arguments show that the center mass of the three particle system lies on the internal bisectors of ∠E and ∠F also. It follows that the center of mass of the wire frame is the point of concurrence of the internal bisectors of the angles of the triangle DEF, which is the incenter of the medial triangle DEF.

Two bodies orbiting their barycenter (red cross) The center of mass plays an important role in astronomy and astrophysics, where it is commonly referred to as the barycenter. The barycenter is the point between two objects where they balance each other; it is the center of mass where two or more celestial bodies orbit each other. When a moon orbits a planet, or a planet orbits a star, both bodies are actually orbiting a point that lies away from the center of the primary (larger) body. For example, the Moon does not orbit the exact center of the Earth, but a point on a line between the center of the Earth and the Moon, approximately 1,710 km (1,062 miles) below the surface of the Earth, where their respective masses balance.

The engine of the Force 1 V10 is placed between the cabin and the front axle, with the engine's center of mass located behind the front axle. This is meant to improve the vehicle's handling by modifying weight distribution. The Force 1 comes standard with a 6-speed manual transmission, but an optional 6-speed paddle-shift automatic would be available on request.

In particular, a non- uniform gravitational field can produce a torque on an object, even about an axis through the center of mass. The center of gravity seeks to explain this effect. Formally, a center of gravity is an application point of the resultant gravitational force on the body. Such a point may not exist, and if it exists, it is not unique.

Newton suggested two experiments to resolve this problem. One is the effects of centrifugal force upon the shape of the surface of water rotating in a bucket, equivalent to the phenomenon of rotational gravity used in proposals for human spaceflight. The second is the effect of centrifugal force upon the tension in a string joining two spheres rotating about their center of mass.

In aeronautics, the keel effect (also known as the pendulum effect or pendulum stability) is the result of the sideforce-generating surfaces being above (or below) the center of mass (which coincides with the center of gravity) in an aircraft. Along with dihedral, sweepback, and weight distribution, keel effect is one of the four main design considerations in aircraft lateral stability.

This allows the golfer to "work the ball" while still giving some advantage based on the lower center of mass as compared to older designs. The slightly reduced mass of some sets also increases clubhead speed allowing for more variation in swing strength and thus carry distance than would be possible with the heavier mass of most game improvement irons.

Biomechanical factors such as mechanical work, stability, and joint or muscle forces may also influence human walking speed. Walking faster requires additional external mechanical work per step. Similarly, swinging the legs relative to the center of mass requires some internal mechanical work. As faster walking is accomplished with both longer and faster steps, internal mechanical work also increases with increasing walking speed.

Ottoman Empire welcomed Jews expelled from Spain & Portugal Some of the Monarchies of Asia Minor and European welcomed expelled Jewish Merchants, scholars and theologians. Divergent Jewish philosophies evolved against the backdrop of new cultures, new languages and renewed theological exchange. Philosophic exploration continued through the Renaissance period as the center-of-mass of Jewish Scholarship shifted to France, Germany, Italy, and Turkey.

In classical mechanics a physical body is collection of matter having properties including mass, velocity, momentum and energy. The matter exists in a volume of three-dimensional space. This space is its extension. Under Newtonian gravity the gravitational field further away than the furthest extent of an object is determined only by the mass and the position of the center of mass.

The engine is in-line with the center of mass to avoid thrust-pitch coupling. It employs a fuselage-top mount, its intakes outside the boundary layer. The aircraft is flown by sidesticks like Lancair aircraft or the Cessna TTx. The first prototype has an experimental Electronic International/Garmin flight deck, but production aircraft will have a Garmin G3000 cockpit.

Running and walking incorporated different biomechanisms. Walking requires an "inverted pendulum" where the body's center of mass is shifted over the extended leg, to exchange potential and kinetic energy with each step. Running involves a "mass spring" mechanism to exchange potential and kinetic energy, with the use of tendons and ligaments. Tendons and ligaments are elastic tissues that store energy.

Molecules have rotational energy owing to rotational motion of the nuclei about their center of mass. Due to quantization, these energies can take only certain discrete values. Rotational transition thus corresponds to transition of the molecule from one rotational energy level to the other through gain or loss of a photon. Analysis is simple in the case of diatomic molecules.

The center of mass of the Jupiter–Sun system lies outside the surface of the Sun, though arguing that Jupiter and the Sun are a double star is not analogous to arguing Pluto-Charon is a double dwarf planet. Jupiter is too light to be a fusor; were it thirteen times heavier, it would achieve deuterium fusion and become a brown dwarf.

All experiments to date agree with the Standard Model of the electron, with no substructure, ring-like or otherwise. The two major approaches are high-energy electron–positron scatteringD. Bourilkov, "Hint for axial-vector contact interactions in the data on e+e− → e+e−(γ) at center-of-mass energies 192–208 GeV", Phys. Rev. D 64, 071701 (2001), Physical Review Online Archive.

SimCraft worked to refine the Center of Mass architecture and with the specific goal of producing a commercial level 2DOF and 3DOF motion simulator. Electromechanical actuation was adopted as the sole medium for motion control, to eliminate air pressure latency and performance issues, and proprietary rotary "knuckle" bearings were developed to form the CORE architecture and create the adaptability of various chassis designs.

Cabell and Bateman, p. 22 Factors such as angular momentum, the moment of inertia, angular acceleration, and the skater's center of mass determines if a jump is successfully completed.Cabell and Bateman, p. 27 Unlike jumping from dry land, which is fundamentally a linear movement, jumping on the ice is more complicated because of angular momentum. For example, most jumps involve rotation.Petkevich, p.

Small size provides many advantages to arboreal species: such as increasing the relative size of branches to the animal, lower center of mass, increased stability, lower mass (allowing movement on smaller branches), and the ability to move through more cluttered habitat. Size relating to weight affects gliding animals such as the reduced weight per snout-vent length for 'flying' frogs.

It is only the lack of total momentum in the system (the system momenta sum to zero) which allows the kinetic energy of the electron to be "weighed". If the electron is stopped and weighed, or the scale were somehow sent after it, it would not be moving with respect to the scale, and again the relativistic and rest masses would be the same for the single electron (and would be smaller). In general, relativistic and rest masses are equal only in systems which have no net momentum and the system center of mass is at rest; otherwise they may be different. The invariant mass is proportional to the value of the total energy in one reference frame, the frame where the object as a whole is at rest (as defined below in terms of center of mass).

Currently, the most commonly proposed definition for a double- planet system is one in which the barycenter, around which both bodies orbit, lies outside both bodies. Under this definition, Pluto and Charon are double dwarf planets, since they orbit a point clearly outside of Pluto, as visible in animations created from images of the New Horizons space probe in June 2015. Under this definition, the Earth–Moon system is not currently a double planet; although the Moon is massive enough to cause the Earth to make a noticeable revolution around this center of mass, this point nevertheless lies well within Earth. However, the Moon currently migrates outward from Earth at a rate of approximately per year; in a few billion years, the Earth–Moon system's center of mass will lie outside Earth, which would make it a double- planet system.

If a BCS superconductor with a ground state consisting of Cooper pair singlets (and center-of-mass momentum q=0) is subjected to an applied magnetic field, then the spin structure is not affected until the Zeeman energy is strong enough to flip one spin of the singlet and break the Cooper pair, thus destroying superconductivity (paramagnetic or Pauli pair breaking). If instead one considers the normal, metallic state at the same finite magnetic field, then the Zeeman energy leads to different Fermi surfaces for spin-up and spin-down electrons, which can lead to superconducting pairing where Cooper pair singlets are formed with a finite center-of-mass momentum q, corresponding to the displacement of the two Fermi surfaces. A non-vanishing pairing momentum leads to a spatially modulated order parameter with wave vector q.

The key component of the system is the concept of using a balanced, center of mass architecture in which the motion chassis rotates about its Center of Gravity (CG). This setup requires a much smaller amount of force to provide a large range of motion, and is different from the Stewart platform type designs, the standard approach in commercial applications over the past several decades, that require large forces for motion. This system of movement is also described by the physics of aircraft. The CG architecture model is intended to mimic a real vehicle's rotational motions since the rotation axes (roll, pitch, and yaw) are mutually perpendicular, always fixed, rotating at or near the actual center of mass (of the sim), and intersecting at a single, static point - as they are in both land and air based vehicles.

It had a significant decrease in the length of the engine compartment allowed the turret to be moved rearwards, which in turn moved its rotation axis and the center of mass to the center of the hull, increased the accuracy of the main gun and decreased a chance that the turret could get stuck after getting hit in the turret ring with a projectile that ricocheted. The thickness of the frontal armor protection more than doubled without disturbing the center of mass or drastically increasing the weight of the tank. T-44-122 prototype during comparative trials against captured German Panther The T-44A officially entered service with the Red Army on 23 November 1944 but the production started in October."armoured.vif2.ru" The original plans were that the factory would produce 300 T-44As a month.

The Laboratory for Elementary-Particle Physics (LEPP) is a high-energy physics laboratory studying fundamental particles and their interactions. In operation below the athletic fields on campus is the 768 meter Cornell Electron Storage Ring (CESR). CESR is an electron-positron collider operating at a center-of-mass energy in the range of 3.5-12 GeV. Completed in 1979, CESR stores beams accelerated by the Cornell Synchrotron.

Villous plaque is characterized by exophytic epicardial thickening, meaning that the growth occurs at the border of the epicardium and not the center of mass. Unlike milk spots and chagasic rosary, inflammatory cells and vasculature are present in villous plaque. Since villous plaque contains inflammatory cells it is reasonable to suspect that these lesions are more recently formed than milk spots or chagasic rosary.

12 kg, 16 kg, and 24 kg kettlebells Unlike traditional dumbbells, a kettlebell's center of mass is extended beyond the hand, similar to Indian clubs or ishi sashi. This facilitates ballistic and swinging movements. Variants of the kettlebell include bags filled with sand, water, or steel shot. The kettlebell allows for swing movements and release moves with added safety and added grip, wrist, arm and core strengthening.

Rubber bumpers, Crumple zones, and safe launch practices can be utilized to minimize damage or injury caused by a falling rocket. Another possible recovery system involves simply using the rocket's fins to slow its descent and is sometimes called backward sliding. By increasing fin size, more drag is generated. If the center of mass is placed forward of the fins, the rocket will nose dive.

In orbit, a spacecraft with one axis much longer than the other two will spontaneously orient so that its long axis points at the planet's center of mass. This system has the virtue of needing no active control system or expenditure of fuel. The effect is caused by a tidal force. The upper end of the vehicle feels less gravitational pull than the lower end.

The inverted pendulum theory directly contradicts the six determinants of gait, another theory for gait analysis. The six determinants of gait predict very high energy expenditure for the sinusoidal motion of the Center of Mass during gait, while the inverted pendulum theory offers the possibility that energy expenditure can be near zero; the inverted pendulum theory predicts that little to no work is required for walking.

The propellants were pressure-fed to the engine by of gaseous helium at , carried in two diameter spherical tanks. The exhaust nozzle engine bell measured long and wide at the base. It was mounted on two gimbals to keep the thrust vector aligned with the spacecraft's center of mass during SPS firings. The combustion chamber and pressurant tanks were housed in the central tunnel.

In climbing of vertical ice, two tools are needed in order for the climber (supported by cramponed feet) to use each tool in turn in maintaining balance with the body's center of mass nearly straight above the toes, while repositioning the other tool to a higher level, before raising the body weight with the legs and thereby setting the stage for repeating the process.

However, the linear type has no restriction in one dimension, because it can roll. Its wheels must not slip, because the movement must be constrained to a straight line. Developments of the planimeter can establish the position of the first moment of area (center of mass), and even the second moment of area. The images show the principles of a linear and a polar planimeter.

Oskar Klein and Walter Gordon proposed the Klein–Gordon equation to describe quantum particles in the framework of relativity. Another important contribution by Gordon was to the theory of the Dirac equation, where he introduced the Gordon decomposition of the current into its center of mass and spin contributions, and so helped explain the g=2 g-factor value in the electron's gyromagnetic ratio.

Its vibration, noise, and tendency to overheat were rectified by 1974. The Vega's suspension, live rear axle, 53.2% front/46.8% rear weight distribution, low center of mass and neutral steering give good handling. Lateral acceleration capacities are 0.90 g (standard suspension) and 0.93 g (RPO F-41 suspension). Steering box and linkage are ahead of the front wheel centerline, with a cushioned two-piece shaft.

Standing posture relies on dynamic rather than static balance. The human center of mass is in front of the ankle, and unlike in tetrapods, the base of support is narrow, consisting of only two feet. A static pose would cause humans to fall forward onto the face. In addition, there are constant external perturbations, such as breezes, and internal perturbations that come from respiration.

The lean moves the body's center of mass further than it can support. In the video, the illusion was achieved using cables and a harness. In October 1993, Jackson and his team patented a method of performing the lean in concert using specially designed shoes that hook into pegs that rise from the stage. Even with the shoes, the move requires good athletic core strength.

For even closer trajectories, gravity anomalies may be important. For a large asteroid (or comet) passing close to the Roche limit, its size, which is inferred from its magnitude, affects not only the Roche limit but also the trajectory because the center of gravitational force on the body deviates from its center of mass resulting in a higher-order tidal force shifting the keyhole.

Each median of a triangle passes through the triangle's centroid, which is the center of mass of an infinitely thin object of uniform density coinciding with the triangle. Thus the object would balance on the intersection point of the medians. The centroid is twice as close along any median to the side that the median intersects as it is to the vertex it emanates from.

Both stars of the close binary are considered to be Solar-type stars that are slightly more massive than the Sun. The two stars differ in effective temperature by only ~250 K and have a mass ratio of 0.91. The two orbit a common center of mass every 3.42 days. Within the spectra of the two stars the Li lines show different equivalent widths.

The influences of increased hormones such as estrogen and relaxin initiate the remodeling of soft tissues, cartilage and ligaments. Certain skeletal joints such as the pubic symphysis and sacroiliac widen or have increased laxity. The addition of mass, particularly around the torso, naturally changes a pregnant mother's center of mass (COM). The change in COM requires pregnant mothers to adjust their bodies to maintain balance.

The tricycle layout reduces the possibility of a ground loop, because the main gear lies behind the center of mass. However, tricycle aircraft can be susceptible to wheel-barrowing. The nosewheel equipped aircraft also is easier to handle on the ground in high winds due to its wing negative angle of attack. Student pilots are able to safely master nosewheel equipped aircraft more quickly.

CLEO has studied two- photon physics, where both an electron and positron radiate a photon. The two photons interact to produce either a vector meson or hadron-antihadron pairs. CLEO published measurements of both the vector meson process and the hadron- antihadron process. CLEO performed an energy scan for center-of-mass energies between 7 GeV and 10 GeV to measure the hadronic cross section ratio.

The two stellar components orbit around their common center of mass, or barycenter, with a period of 56.3 years and an eccentricity of 0.766. The semi-major axis of their orbit spans an angle of 1.06 arcseconds, which corresponds to a physical dimension of 16.5 AU. The plane of their orbit is inclined by an angle of about 39° to the line-of-sight from the Earth.

In geometry, the Spieker center is a special point associated with a plane triangle. It is defined as the center of mass of the perimeter of the triangle. The Spieker center of a triangle ABC is the center of gravity of a homogeneous wire frame in the shape of triangle ABC. The point is named in honor of the 19th-century German geometer Theodor Spieker.

A sphere rotating about an axis A rotation is a circular movement of an object around a center (or point) of rotation. A three-dimensional object can always be rotated about an infinite number of imaginary lines called rotation axes ( ). If the axis passes through the body's center of mass, the body is said to rotate upon itself, or spin. A rotation around an external point, e.g.

Diagram of the principles of operation of a Weeble. The grey material is of a higher density than the red material, causing the center of mass of the object (labelled C) to be very low. This means that when the Weeble is wobbled, as in position B, the center of mass will be on the other side of the pivot point (where the Weeble is in contact with the ground), and so gravity will cause it to return to an upright position. Weeble is shaped like an egg—in order for the physics principles to work as intended, the shape must have a bottom which is a more or less smooth (unfaceted) hemisphere (to allow the Weeble to roll) and from the central vertical axis the shape must be nearly cylindrically symmetrical (that is, any plane cut through the vertical axis line must produce close to the same profile).

Consequently, another modification is the concept of the center of mass of a system, which is straightforward to define in classical mechanics but much less obvious in relativity – see relativistic center of mass for details. The equations become more complicated in the more familiar three- dimensional vector calculus formalism, due to the nonlinearity in the Lorentz factor, which accurately accounts for relativistic velocity dependence and the speed limit of all particles and fields. However, they have a simpler and elegant form in four-dimensional spacetime, which includes flat Minkowski space (SR) and curved spacetime (GR), because three-dimensional vectors derived from space and scalars derived from time can be collected into four vectors, or four-dimensional tensors. However, the six component angular momentum tensor is sometimes called a bivector because in the 3D viewpoint it is two vectors (one of these, the conventional angular momentum, being an axial vector).

An increasing number of wireless devices with mutually incompatible data and screen formats make it even more difficult to achieve the objective "create once, publish many". The Internet is quickly becoming the center of mass media. Everything is becoming accessible via the internet. Rather than picking up a newspaper, or watching the 10 o'clock news, people can log onto the internet to get the news they want, when they want it.

Neutral buoyancy simulates the weightless environment of space. First equipment is lowered into the pool using an overhead crane. Suited astronauts then get in the tank and support divers add weight to the astronauts so that they experience no buoyant force and no rotational moment about their center of mass. One downside of using neutral buoyancy to simulate microgravity is the significant amount of drag presented by water.

Crabwalking builds triceps endurance"Crab Walk Exercise" at CombatFitness.co.uk and arm and leg strength, and is a recommended exercise of various school athletic departments and soccer organizations, such as USA football. USA The crab crawl is also useful for descending steep slopes with poor traction. Its feet-first orientation ensures a low center of mass to prevent tumbling, while the inverted posture allows one to see where they're going.

In late 2012, S&S; Worldwide unveiled a new concept called Free Spin which features a similar ride to Intamin ZacSpin. Each vehicle features two seating rows, and each row rotates independently. Because the axis of rotation is at the center of mass of each guest, rider comfort is significantly improved. Like with ZacSpin, Seats spin freely, but during several track sections a system of magnets forces a controlled inversion.

In fact, this process is repeated thousands of times. At the end, a distribution of outcomes is available which shows not only the most likely estimate but what ranges are reasonable too. The most likely estimate is given by the distribution curve's (formally known as the Probability density function) center of mass which is typically also the peak(mode) of the curve, but may be different e.g. for asymmetric distributions.

Such bosons were also measured using proton-antiproton annihilation. The combined rest energy of those particles amounts to approximately 0.938 GeV each. The Super Proton Synchrotron accelerated those particle up to relativistic velocities and energies of approximately 270 GeV each, so that the center of mass energy at the collision reaches 540 GeV. Thereby, quarks and antiquarks gained the necessary energy and momentum to annihilate into W and Z bosons.

Measurements were done on proton-antiproton collisions of 540 GeV center-of-mass energy, with the results being published in November 1983. Later, under the name of UA5/2, data was recorded from 900 GeV collisions. No indication of Centauro production was observed, but an upper limit on the production was obtained. The experimental setup consisted of two large streamer chambers which were placed above and below the SpS beam pipe.

Large overhangs contribute to large vehicle dimensions, and the associated advantages of size. On front-engined saloon/sedans, measuring rear overhang is helpful in predicting the size of the trunk. For these same vehicles, large front overhangs can accommodate larger engines. The Porsche 911, produced since 1964, has always contained its entire flat-6 engine within its rear overhang, with the center of mass of the engine outside of the wheelbase.

Gyropter Papin et Rouilly thumb A monocopter or gyropter is a rotorcraft that uses a single rotating blade. The concept is similar to the whirling helicopter seeds that fall from some trees. The name gyropter is sometimes applied to monocopters in which the entire aircraft rotates about its center of mass as it flies. The name "monocopter" has also been applied to the personal jet pack constructed by Andreas Petzoldt.

Example of geometric median (in yellow) of a series of points. In blue the Center of mass. The geometric median of a discrete set of sample points in a Euclidean space is the point minimizing the sum of distances to the sample points. This generalizes the median, which has the property of minimizing the sum of distances for one-dimensional data, and provides a central tendency in higher dimensions.

Hoche after her 1898 reconstruction The ship was modified several times over the course of her career to correct her stability deficiencies. Six of her 138 mm guns were removed by 1895 in an effort to lighten her superstructure. In 1898, Hoche underwent a more thorough reconstruction to remedy her instability and upgrade her armament and propulsion system. Her superstructure was reduced significantly to lower her center of mass.

There are documentaries of the emigration and of the exile (rescued some of them at the end of the 20th century). The more distinguished figure is Carlos Velo (1909–1988). Before being exiled during the Spanish Civil War, he made documentary shorts for afterwards pass to Mexico where they consider him a director of Mexican cinema. In the eighties it was a center of mass of tributes and considered a pioneer.

Because of the movement of Earth around the Earth–Moon center of mass, the apparent path of the Sun wobbles slightly, with a period of about one month. Because of further perturbations by the other planets of the Solar System, the Earth–Moon barycenter wobbles slightly around a mean position in a complex fashion. The ecliptic is actually the apparent path of the Sun throughout the course of a year. , p.

A mixture of two approximately equal mass normal distributions has a negative kurtosis since the two modes on either side of the center of mass effectively reduces the tails of the distribution. A mixture of two normal distributions with highly unequal mass has a positive kurtosis since the smaller distribution lengthens the tail of the more dominant normal distribution. Mixtures of other distributions require additional parameters to be estimated.

There are a few different causes for gravitaxis. Many microorganisms have receptors like statocysts that allow them to sense the direction of gravity and to adjust their orientation accordingly. However, gravitaxis can result also from a purely physical mechanism so that organs for sensing the direction of gravity are not necessary. An example is given by microorganisms with a center of mass that is shifted to one end of the organism.

In wheeled vehicles, load transfer is the measurable change of load borne by different wheels during acceleration (both longitudinal and lateral). This includes braking, and deceleration (which is an acceleration at a negative rate). No motion of the center of mass relative to the wheels is necessary, and so load transfer may be experienced by vehicles with no suspension at all. Load transfer is a crucial concept in understanding vehicle dynamics.

His technique uses simple machines such as levers aided by counterweights and pivots. He says that he has successfully singlehandedly "walked" a twenty-ton barn and multi- thousand-pound concrete blocks using a beam lever and two pivots beneath the object and near the center of mass. These techniques might be comparable to those used by Edward Leedskalnin when he had single-handedly constructed his massive Coral Castle in Florida.

The mid-engine, rear-wheel drive layout (abbreviated as MR layout) is one where the rear wheels are driven by an engine placed just in front of them, behind the passenger compartment. In contrast to the rear-engined RR layout, the center of mass of the engine is in front of the rear axle. This layout is typically chosen for its low moment of inertia and relatively favorable weight distribution.

They are both G-type main sequence stars slightly less massive than the Sun, with spectral types G7V and G8V respectively. They complete an orbit around their center of mass approximately every 6 days. Using Gaia parallax, instead, the pair formed by the primary and the secondary is much closer than previous measures, at an estimated distance of 175 light years. The two pairs, then, may be not gravitationally bound.

Wadcutter or Flathead pellets A .177 (4.5mm) caliber "Wadcutter" pellet next to a stick of chewing gum The most popular ammunition used in rifled air guns is the wasp-waisted diabolo pellet, which has two sections – a solid front portion called the "head", which contains the center of mass and is available in a variety of shapes and styles such as flat (wadcutter), round (domed), cone-shaped (pointed) and pitted (hollow point); and a hollowed, thin-walled conical rear portion called the "skirt", which expands and fully engages the bore to provide a good seal and thus allows maximal efficiency in pellet propulsion during shooting. In flight, the skirt has greater drag-to- weight ratio than the head and exerts a rearward pull behind the center of mass, similar to that of a shuttlecock. This produces a phenomenon known as drag stabilization, which helps to counteract yawing and maintain a consistent flight path.

He considers a conceptual small cell in a situation of continuous-flow as a system defined in the so-called Lagrangian way, moving with the local center of mass. The flow of matter across the boundary is zero when considered as a flow of total mass. Nevertheless, if the material constitution is of several chemically distinct components that can diffuse with respect to one another, the system is considered to be open, the diffusive flows of the components being defined with respect to the center of mass of the system, and balancing one another as to mass transfer. Still there can be a distinction between bulk flow of internal energy and diffusive flow of internal energy in this case, because the internal energy density does not have to be constant per unit mass of material, and allowing for non- conservation of internal energy because of local conversion of kinetic energy of bulk flow to internal energy by viscosity.

Two separate regions of condensation are critical. At the pointed tip of the spore (the hilum) closest to the supporting basidium, Buller's drop accumulates as a large, almost spherical water droplet. At the same time, condensation occurs in thin film on the adaxial face of the spore. When these two bodies of water coalesce, the release of surface tension and the sudden change in the center of mass leads to sudden discharge of the basidiospore.

The centers of gravity defined above are not fixed points on the body; rather, they change as the position and orientation of the body changes. This characteristic makes the center of gravity difficult to work with, so the concept has little practical use.; . When it is necessary to consider a gravitational torque, it is easier to represent gravity as a force acting at the center of mass, plus an orientation-dependent couple.

For a higher ride height, the center of mass of the car is higher, which makes for less precise and more dangerous handling characteristics (most notably, the chance of rollover is higher). Higher ride heights will typically adversely affect aerodynamic properties. This is why sports cars typically have very low clearances, while off-road vehicles and SUVs have higher ones. Two well-known extremes of each are the Ferrari F40 and the Hummer.

Let the system be subject to external forces that produce no torque with respect to its center of mass in its (instantaneous) rest frame. The condition of "no torque" is necessary to isolate the phenomenon of Thomas precession. As a simplifying assumption one assumes that the external forces bring the system back to its initial velocity after some finite time. Fix a Lorentz frame such that the initial and final velocities are zero.

In particle physics the Froissart bound,Froissart, Marcel (1961). Asymptotic Behavior and Subtractions in the Mandelstam Representation. Physical Review 123 (3): 1053-1057. or Froissart limit, is a generic constraint that the total scattering cross section of two colliding high-energy particles cannot increase faster than c×ln2(s), with c a normalization constant and s the square of the center-of-mass energy (s is one of the three Mandelstam variables).

The RoboSeed Nano controllable monocopter UAV Monocopters, in which the entire aircraft rotates about its center of mass as it flies, present advantages and challenges as unmanned aerial vehicles (UAVs) to the designer. As highly centripetal machines, they cannot be manned. The first of these monocopters were constructed by Dr. Charles W. McCutchen and powered by reciprocating model airplane enginesMcCutchen, C.W., 1954, "Charles McCutchen's Flying Machines" Aeromodeller, 19, 222, p.350 ff.

Wheelbase is the horizontal distance between the centers (or the ground contact points) of the front and rear wheels. Wheelbase is a function of rear frame length, steering axis angle, and fork offset. It is similar to the term wheelbase used for automobiles and trains. Wheelbase has a major influence on the longitudinal stability of a bike, along with the height of the center of mass of the combined bike and rider.

Figure 2: Two spheres tied with a string and rotating at an angular rate ω. Because of the rotation, the string tying the spheres together is under tension. Newton also proposed another experiment to measure one's rate of rotation: using the tension in a cord joining two spheres rotating about their center of mass. Non-zero tension in the string indicates rotation of the spheres, whether or not the observer thinks they are rotating.

The fundamental plane is the plane of the Earth's orbit, called the ecliptic plane. There are two principal variants of the ecliptic coordinate system: geocentric ecliptic coordinates centered on the Earth and heliocentric ecliptic coordinates centered on the center of mass of the Solar System. The geocentric ecliptic system was the principal coordinate system for ancient astronomy and is still useful for computing the apparent motions of the Sun, Moon, and planets.Aaboe, Asger.

In mathematical physics, the Gordon decomposition (named after Walter Gordon) of the Dirac current is a splitting of the charge or particle-number current into a part that arises from the motion of the center of mass of the particles and a part that arises from gradients of the spin density. It makes explicit use of the Dirac equation and so it applies only to "on-shell" solutions of the Dirac equation.

Highracers are generally more maneuverable than lowracers since their higher center of mass make them easier to balance at lower speeds. Given the same seating position they may be faster than lowracers, since it is widely believed that rolling resistance is inversely proportional to wheel diameter. However, lowracer proponents reply that their design is faster due to aerodynamics. The reasoning is that the riders body is in line with the wheels, reducing drag.

As the instability grows, the center of mass of the fluid is lowered. In growing waves in the atmosphere, cold air moving downwards and equatorwards displaces the warmer air moving polewards and upwards. Baroclinic instability can be investigated in the laboratory using a rotating, fluid filled annulus. The annulus is heated at the outer wall and cooled at the inner wall, and the resulting fluid flows give rise to baroclinically unstable waves.

The pulsar and its neutron star companion both follow elliptical orbits around their common center of mass. The period of the orbital motion is 7.75 hours, and the two neutron stars are believed to be nearly equal in mass, about 1.4 solar masses. Radio emissions have been detected from only one of the two neutron stars. The minimum separation at periastron is about 1.1 solar radii; the maximum separation at apastron is 4.8 solar radii.

In the case of a toy top, its weight is acting downwards from its center of mass and the normal force (reaction) of the ground is pushing up on it at the point of contact with the support. These two opposite forces produce a torque which causes the top to precess. The response of a rotating system to an applied torque. When the device swivels, and some roll is added, the wheel tends to pitch.

Some models were shipped with a short Vibrola Maestro Tremolo. This 1967 model is now the standard for the Flying V although the earlier design is periodically reissued. Like other Gibson guitars the Flying V's headstock is angled at 17 degrees to increase string pressure on the nut to increase the amount of sustain. The design of the V places the pickups near the center of mass of the entire guitar, further enhancing sustain.

Ground forces and body pitching movement is less of an issue in the walking gait, where the position of the body's center of mass varies less, making walking an inherently more stable gait. In response to the destabilization of the running gait, the human body appears to have evolved adaptations to increase stabilization, as well as for the mass-spring mechanism in general. These adaptations, described below, are all evidence for selection for endurance running.

The center of mass, usually called the center of gravity or "CG", is the balance point of an aircraft. If suspended at this point and allowed to rotate, a body (aircraft) will be balanced. The front-to-back location of the CG is of primary importance for the general stability of the aircraft, but the vertical location has important effects as well. The vertical location of the CG changes the amount of dihedral effect.

An active attitude control system (ACS) is essential for a sail craft to achieve and maintain a desired orientation. The required sail orientation changes slowly (often less than 1 degree per day) in interplanetary space, but much more rapidly in a planetary orbit. The ACS must be capable of meeting these orientation requirements. Attitude control is achieved by a relative shift between the craft's center of pressure and its center of mass.

In celestial mechanics and the mathematics of the -body problem, a central configuration is a system of point masses with the property that each mass is pulled by the combined gravitational force of the system directly towards the center of mass, with acceleration proportional to its distance from the center. Central configurations may be studied in Euclidean spaces of any dimension, although only dimensions one, two, and three are directly relevant for celestial mechanics.

The EMFF system is most applicable in cases where multiple spacecraft are free-flying relative to one another and there is no need to control the center of mass of the system. NASA’s Terrestrial Planet Finder (TPF) mission and space telescope assembly are just two such types of missions. EMFF provides the foremost advantage of reduced dependence on consumables.D. W. Kwon, Electromagnetic Formation Flight of Satellite Arrays, Massachusetts Institute of Technology, SERC #02-05, chap.

However, the results for point particles can be used to study such objects by treating them as composite objects, made of a large number of collectively acting point particles. The center of mass of a composite object behaves like a point particle. Classical mechanics uses common sense notions of how matter and forces exist and interact. It assumes that matter and energy have definite, knowable attributes such as location in space and speed.

It is fitting that Li et al. (2016) use ELVIS to model how Eridanus II's center of mass is moving this way, while also transversely rotating that way, as only the King could manage! For reasons to be discussed in the concluding section, most researchers now believe that Eridanus II is an extremely long-period (i.e., several billion years per orbit) satellite of the Milky Way, probably beginning only its second approach to our galaxy.

McChristian, pp.1–72 A target becomes available for B-52 strike when it can be pinpointed in a one square kilometer spot.Melyan, p.56 On November 11, intelligence source notified Brigadier Knowles all three NVA regiments had assembled within one square kilometer area with the 66th being the last one reaching that condition (center of mass Vic YA 9104), and the 32nd (YA 820070) and the 33rd (YA 940010) less than one square kilometer.

Cargo planes are designed to carry large loads long distances at speed. In order to stay relatively stable they must prevent loads from breaking free or shifting, because unbalanced loads on an aircraft can lead to a major catastrophe. The reason for this, is if the center of mass leaves an invisible box, called the flight zone, the plane is no longer stable and the pilots have to fight the aircraft to stay aloft.

This circle is known as the Spieker circle. The Spieker center is also located at the intersection of the three cleavers of triangle ABC. A cleaver of a triangle is a line segment that bisects the perimeter of the triangle and has one endpoint at the midpoint of one of the three sides. Each cleaver contains the center of mass of the boundary of triangle ABC, so the three cleavers meet at the Spieker center.

The hunched position that often results from complete spinal fusion can have an effect on a person's gait. Increased spinal kyphosis will lead to a forward and downward shift in center of mass (COM). This shift in COM has been shown to be compensated by increased knee flexion and ankle dorsiflexion. The gait of someone with ankylosing spondylitis often has a cautious pattern because they have decreased ability to absorb shock, and they cannot see the horizon.

In their 2015 re-description of Sigilmassasaurus, Evers and colleagues argued that Sigilmassasaurus was in fact a distinct genus from Spinosaurus, and therefore doubted whether the material assigned to Spinosaurus by Ibrahim et. al. should be assigned to Spinosaurus or Sigilmassasaurus. In 2018, an analysis by Henderson found that Spinosaurus probably was competent at bipedal terrestrial locomotion; the center of mass was instead found to be close to the hips, allowing Spinosaurus to stand upright like other bipedal theropods.

Setbacks on the Pyramid of Djoser, Saqqara, Egypt A setback, sometimes called step-back, is a step-like recession in a wall. Setbacks were initially used for structural reasons, but now are often mandated by land use codes, or are used for aesthetic reasons. In densely built-up areas, setbacks also help get more daylight and fresh air to the street level. Importantly, a setback helps lower the building's center of mass, making it more stable.

One of the most pervasive effects of aging is the loss of cutaneous and pressure sensation, which has been correlated with impaired balance control and increased risk of falling.Verrillo, RT. The effects of aging on the sense of touch. Sensory Research Multimodal Perspectives. Hillsdale, NJ; Lawrence Erlbaum Associates; 1993:285-298 This is because for an upright stance, the center of mass(COM) of the body must be positioned over the base of support (BOS) established by the feet.

Running economy also depends on many innate characteristics with some body characteristics naturally giving runners an advantage. Some of these include height, limb length, and body mass distribution in certain areas of the body. Limbs are a greater distance from a person’s center of mass, so they have greater rotational inertia compared to the rest of the body. As a result, limb movements require more energy to move, so their morphology plays a role in running economy.

The static stability of a spherical section is assured if the vehicle's center of mass is upstream from the center of curvature (dynamic stability is more problematic). Pure spheres have no lift. However, by flying at an angle of attack, a spherical section has modest aerodynamic lift thus providing some cross-range capability and widening its entry corridor. In the late 1950s and early 1960s, high-speed computers were not yet available and computational fluid dynamics was still embryonic.

One way to define the center of gravity of a body is as the unique point in the body if it exists, that satisfies the following requirement: There is no torque about the point for any positioning of the body in the field of force in which it is placed. This center of gravity exists only when the force is uniform, in which case it coincides with the center of mass. This approach dates back to Archimedes.

The SpS would accelerate the beams to 450 GeV, keeping them as this energy for a time limited by the heating of the magnets, then decelerate the beams to 100 GeV. The pulsing was operated in such a way that the average dispersion of power in the magnets did not exceed the level of operation at 315 GeV. The SpS occasionally ran pulsed operation after 1985, obtaining collisions at a center-of-mass energy of 900 GeV.

In mathematics and statistics, the Fréchet mean is a generalization of centroids to metric spaces, giving a single representative point or central tendency for a cluster of points. It is named after Maurice Fréchet. Karcher mean is the renaming of the Riemannian Center of Mass construction developed by Karsten Grove and Hermann Karcher... On the real numbers, the arithmetic mean, median, geometric mean, and harmonic mean can all be interpreted as Fréchet means for different distance functions.

UA8 experiment was a high-energy physics experiment at the Proton-Antiproton Collider at CERN. The proposal for the experiment was done by physicists at the University of California, and it was approved in April 1985. Its spokesperson was Peter Schlein. The aim of the experiment was to search for and study jets in high mass collisions at 630 GeV center-of-mass energy, in order to elucidate the nature of the pomeron and its possible particle structure.

The Antiproton Accumulator (AA) was an infrastructure connected to the Proton–Antiproton Collider (SpS) – a modification of the Super Proton Synchrotron (SPS) – at CERN. The AA was built in 1979 and 1980, for the production and accumulation of antiprotons. In the SpS the antiprotons were made to collide with protons, achieving collisions at a center of mass energy of app. 540 GeV (later raised to 630 GeV and finally, in a pulsed mode, to 900 GeV).

At an altitude of the rocket rolled to the correct flight azimuth and then gradually pitched down until 38 seconds after second stage ignition. This pitch program was set according to the prevailing winds during the launch month. The four outboard engines also tilted toward the outside so that in the event of a premature outboard engine shutdown the remaining engines would thrust through the rocket's center of mass. The Saturn V reached at over in altitude.

In a cannon, the trunnions are two projections cast just forward of the center of mass of the cannon and fixed to a two-wheeled movable gun carriage.Duffy, Chris (1979) Siege Warfare: The Fortress in the Early Modern World 1494-1660. Routledge & Kegan Paul. As they allowed the muzzle to be raised and lowered easily, the integral casting of trunnions is seen by military historians as one of the most important advances in early field artillery.

Since the Sun's mass is so much larger than Earth's, the Sun does not generally appear to react to the pull of Earth, but in fact it does, as demonstrated in the animation (not to precise scale). A correct way of describing the combined motion of both objects (ignoring all other celestial bodies for the moment) is to say that they both orbit around the center of mass, referred to in astronomy as the barycenter, of the combined system.

The name CLEO is a play on words and not an acronym. The name was chosen because it is short for Cleopatra due to her relationship with Caesar. Collisions occurred at a center of mass energy ranging from 3.5 GeV to 12 GeV at its peak. This turned out to be ideal for the study of the B meson and data from these collisions provided physicists with many new insights into the physics of fundamental particles.

The primary disadvantage to this system is the disruption of the point of aim due to several factors such as: the center of mass changing during the action cycle, abrupt stops at the beginning and end of bolt carrier travel, and the use of the barrel as a fulcrum to drive the bolt back. Also, due to the greater mass of moving parts, more gas is required to operate the system that, in turn, requires larger operating parts.

The flight control was carried out with the help of four carbon jet vanes, located in the nozzles of the rocket motors. The autonomous guidance and control system used center of mass normal and lateral stabilization devices, a velocity control system and a computer-assisted automatic range control system. The R-12 was deployed at both soft launch pads and hard silos. Standard thermonuclear explosive charges 2.3 Mt. Explosive charges or chemical weapons could have been used as well.

Due to forces that the Sun and Moon exert, Earth's equatorial plane moves with respect to the celestial sphere. Earth rotates while the ECI coordinate system does not. Earth-centered inertial (ECI) coordinate frames have their origins at the center of mass of Earth and do not rotate with respect to the stars. ECI frames are called inertial, in contrast to the Earth-centered, Earth-fixed (ECEF) frames, which remain fixed with respect to Earth's surface in its rotation.

In physics, circular motion is a movement of an object along the circumference of a circle or rotation along a circular path. It can be uniform, with constant angular rate of rotation and constant speed, or non-uniform with a changing rate of rotation. The rotation around a fixed axis of a three- dimensional body involves circular motion of its parts. The equations of motion describe the movement of the center of mass of a body.

Since and N have the same number of electrons, is isoelectronic with ammonia. As shown in the images above, has a trigonal pyramidal molecular geometry with the oxygen atom at its apex. The bond angle is approximately 113°, and the center of mass is very close to the oxygen atom. Because the base of the pyramid is made up of three identical hydrogen atoms, the molecule's symmetric top configuration is such that it belongs to the point group.

Mass point geometry, colloquially known as mass points, is a geometry problem- solving technique which applies the physical principle of the center of mass to geometry problems involving triangles and intersecting cevians.Rhoad, R., Milauskas, G., and Whipple, R. Geometry for Enjoyment and Challenge. McDougal, Littell & Company, 1991. All problems that can be solved using mass point geometry can also be solved using either similar triangles, vectors, or area ratios, but many students prefer to use mass points.

Changes in horizontal location between NAD27 and NAD83 To address these, a new datum was developed, designated NAD83. It replaced the Clarke spheroid with a new ellipsoid, the Geographic Reference System 1980, centered at the Earth's center of mass as determined by the Bureau International de l'Heure. The new datum was based on adjustment of 250,000 points, including 600 satellite Doppler stations. NAD83 was officially adopted by the U.S. government in 1989, and by the Canadian government in 1990.

With expulsion from Spain came the dissemination of Jewish philosophical investigation throughout the Mediterranean Basin, Northern Europe and the Western Hemisphere. The center-of-mass of Rationalism shifted to France, Italy, Germany, Crete, Sicily and Netherlands. Expulsion from Spain and the coordinated pogroms of Europe resulted in the cross-pollination of variations on Rationalism incubated within diverse communities. This period is also marked by the intellectual exchange among leaders of the Christian Reformation and Jewish scholars.

Power push-over (Buntover) is the action of an aircraft, typically a gyroplane, whose propeller thrust line is above the center of gravity and lacks an adequate horizontal stabilizer to pitch forward. Power push-over is caused by the creation of a torque around the center of mass of the gyroplane by the force of the propeller and unloading of the rotor. Unloading of the rotor and subsequent power push-over can be caused by excessive pilot-induced oscillations.

The rotating concept. If the orbital velocity and the tether rotation rate are synchronized, the tether tip moves in a cycloid curve. At the lowest point it is momentarily stationary with respect to the ground, where it can 'hook' a payload and swing it into orbit. By rotating the tether around the orbiting center of mass in a direction opposite to the orbital motion, the speed of the hook relative to the ground can be reduced.

John Gaughan described how the trick works in US Patent #5,354,238. According to the patent, the performer is supported by two fan-shaped arrays of fine wires that remain invisible to the viewing audience. The wires are about mm thick, and support about 10 kg each; the arrays contain more than enough wires to support the performer's weight. The wire arrays are mounted at the hips, near the human center of mass, to a harness worn under the clothing.

A Naginatajutsu Tournament in Brazil, organised by the Confederação Brasileira de Kobudo. Naginata can be used to batter, stab, or hook an opponent,Katz 2009 but due to their relatively balanced center of mass, are often spun and turned to proscribe a large radius of reach. The curved blade provides a long cutting surface without increasing the overall length of the weapon. Historically, the naginata was often used by foot soldiers to create space on the battlefield.

The space occupied by a polymer molecule is generally expressed in terms of radius of gyration, which is an average distance from the center of mass of the chain to the chain itself. Alternatively, it may be expressed in terms of pervaded volume, which is the volume spanned by the polymer chain and scales with the cube of the radius of gyration.Rubinstein, p. 13 The simplest theoretical models for polymers in the molten, amorphous state are ideal chains.

To positionally compensate the additional load due to the pregnancy, pregnant mothers often extend their lower backs. As the fetal load increases, women tend to arch their lower backs, specifically in the lumbar region of their vertebral column to maintain postural stability and balance. The arching of the lumbar region is known as lumbar lordosis, which recovers the center of mass into a stable position by reducing hip torque. According to a study conducted by Whitcome, et al.

For the same object, different axes of rotation will have different moments of inertia about those axes. In general, the moments of inertia are not equal unless the object is symmetric about all axes. The moment of inertia tensor is a convenient way to summarize all moments of inertia of an object with one quantity. It may be calculated with respect to any point in space, although for practical purposes the center of mass is most commonly used.

The term primary is often used to avoid specifying whether the object near the barycenter is a planet, a star, or any other astronomical object. In this sense, the word primary is always used as a noun. Motion of the Solar System's barycenter relative to the Sun The center of mass is the average position of all the objects weighed by mass. The Sun is so massive that the Solar System's barycenter lies very near the Sun's center.

The "approach" is the final canter stride before the jump, during which the horse places all four legs for the optimal take-off. The horse reaches forward and down with his neck to lower the forehand and his center of mass. The forelegs are propped or strutted out in front of the body. This relatively sudden braking action allows momentum to carry the hindlegs further under the body of the horse than would be otherwise possible.

C/1999 F1 (Catalina) is one of the longest known long-period comets. It was discovered on March 23, 1999, by the Catalina Sky Survey. The comet has an observation arc of 2,360 days allowing a good estimate of the orbit. The orbit of a long-period comet is properly obtained when the osculating orbit is computed at an epoch after leaving the planetary region and is calculated with respect to the center of mass of the Solar System.

The relaxed solution of -means clustering, specified by the cluster indicators, is given by principal component analysis (PCA). The intuition is that k-means describe spherically shaped (ball-like) clusters. If the data has 2 clusters, the line connecting the two centroids is the best 1-dimensional projection direction, which is also the first PCA direction. Cutting the line at the center of mass separates the clusters (this is the continuous relaxation of the discrete cluster indicator).

Its origin is at the center of mass of the whole earth including the oceans and atmosphere. New ITRF solutions are produced every few years, using the latest mathematical and surveying techniques to attempt to realize the ITRS as precisely as possible. Due to experimental error, any given ITRF will differ very slightly from any other realization of the ITRF. The difference between the latest WGS 84 and the latest ITRF (as of 2006) is only a few centimeters.

A tether is not a spherical object, and has significant extent. This means that as an extended object, it is not directly modelable as a point source, and this means that the center of mass and center of gravity are not usually colocated. Thus the inverse square law does not apply except at large distances, to the overall behaviour of a tether. Hence the orbits are not completely Keplerian, and in some cases they are actually chaotic.

Irregularly shaped, non-rotationally-symmetric discs with an offset center of mass may also cause damaging vibration if played in computer CD drives, which can operate at a much higher rotational velocity than stand-alone audio CD players. Some irregularly shaped discs work with tray-loading CD drives if they include a circular ridge on their underside that centers them on the part of the tray designed to hold 80 mm CDs, if the tray has such a feature.

Computers and motors inside of the device keep the Robstep upright when powered on with balancing enabled. A user commands the Robstep to go forward by shifting their weight forward on the platform, and backward by shifting their weight backward. The Robstep detects, as it balances, the change in its center of mass, and first establishes and then maintains a corresponding speed, forward or backward. Gyroscopic sensors and fluid-based level sensors detect the weight shift.

This similarity between abelisaurids and carcharodontosaurids means that a definitive match between the Brazilian fossil and carcharodontosaurids cannot be made. Allosauroids had long, narrow skulls, large orbits, three-fingered hands, and usually had "horns" or ornamental crests on their heads. Although allosauroids vary in size, the group maintains a similar center of mass and hip position on their bodies. Allosauroids also exhibit reptilian-style immune systems, secreting fibrin at injured sites to prevent infections from spreading through the bloodstream.

Diagram showing how an exoplanet's orbit changes the position and velocity of a star as they orbit a common center of mass. In many binary stars, the orbital motion usually causes radial velocity variations of several kilometers per second (km/s). As the spectra of these stars vary due to the Doppler effect, they are called spectroscopic binaries. Radial velocity can be used to estimate the ratio of the masses of the stars, and some orbital elements, such as eccentricity and semimajor axis.

The MVNX format is a human-readable open XML based format for storing Xsens MVN motion capture data. The format contains the 3D positions and orientations of all segments captured with Xsens MVN. In addition, the format includes several other variables to be exported such as joint angles, segment velocity and free acceleration, center of mass trajectory and calibrated sensor data of the individual motion trackers. MVNX data can also be imported into leading software programs including MATLAB and Excel.

A 12-gauge shotgun, nominally , can range from a tight to an extreme overbore of . Some also claim an increased velocity with the overbored barrels, up to , which is due to the larger swept volume of the overbored barrel. Once only found in expensive custom shotguns, overbored barrels are now becoming common in mass-marketed guns. Aftermarket backboring is also commonly done to reduce the weight of the barrel, and move the center of mass backwards for a better balance.

Due to conservation of energy, only magnetic monopoles with masses less than half of the center of mass energy of the colliding particles can be produced. Beyond this, very little is known theoretically about the creation of magnetic monopoles in high energy particle collisions. This is due to their large magnetic charge, which invalidates all the usual calculational techniques. As a consequence, collider based searches for magnetic monopoles cannot, as yet, provide lower bounds on the mass of magnetic monopoles.

Several different approaches have been used to develop robots that have the ability to climb vertical surfaces. One approach mimics the movements of a human climber on a wall with protrusions; adjusting the center of mass and moving each limb in turn to gain leverage. An example of this is Capuchin, built by Dr. Ruixiang Zhang at Stanford University, California. Another approach uses the specialized toe pad method of wall-climbing geckoes, which can run on smooth surfaces such as vertical glass.

In primates, bipedalism is often associated with food gathering and transport. In lizards, it has been debated whether bipedal locomotion is an advantage for speed and energy conservation or whether it is governed solely by the mechanics of the acceleration and lizard's center of mass. Facultative bipedalism is often divided into high- speed (lizards) and low-speed (gibbons), but some species cannot be easily categorized into one of these two. Facultative bipedalism has also been observed in cockroaches and some desert rodents.

Pluto and its moon Charon are often described as a binary system. When binary minor planets are similar in size, they may be called "binary companions" instead of referring to the smaller body as a satellite. Good examples of true binary companions are the 90 Antiope and the 79360 Sila–Nunam systems. Pluto and its largest moon Charon are sometimes described as a binary system because the barycenter (center of mass) of the two objects is not inside either of them.

As a bike leans, the tires' contact patches move farther to the side causing wear. The portions at either edge of a motorcycle tire that remain unworn by leaning into turns is sometimes referred to as . The finite width of the tires alters the actual lean angle of the rear frame from the ideal lean angle described above. The actual lean angle between the frame and the vertical must increase with tire width and decrease with center of mass height.

An object's center of mass certainly "exists" in some sense, but not in the same sense in which the object itself does. In philosophy, a construct is an object which is ideal, that is, an object of the mind or of thought, meaning that its existence may be said to depend upon a subject's mind. This contrasts with any possibly mind-independent objects, the existence of which purportedly does not depend on the existence of a conscious observing subject.Bunge, M. 1974.

The Kaiserglocke was the largest free-swinging bell in history. The 24-tonne St. Petersglocke ("Bell of St. Peter", "'" in the Kölsch language or in common parlance known as "Dicker Pitter"), was cast in 1922 and was the largest free-swinging bell in the world, until a new bell was cast in Innsbruck for the People's Salvation Cathedral in Bucharest in Romania.The World Peace Bell in Newport, Kentucky is larger, but turns around its center of mass rather than its top.

Jalowiczor has taken part in several research projects as an amateur, including work with exoplanets, brown dwarfs, comets and Mars. He is a member of South Yorkshire's Mexborough and Swinton Astronomical Society, and has given several talks there on the various research projects volunteered for example on his work with Planet Four, a citizen science project. Two stars of different size orbiting the center of mass. The spectrum can be seen to split depending on the position and velocity of the stars.

One of the "determinants" is the lateral movement of the pelvis and excessive movement at the pelvis can be corrected by the position of the foot and leg.Saunders, MB; Inman, VT; Eberhart, HD (1953). "The major determinants in normal and pathological gait". J Bone and Joint Surgery. 35-A(3): 543-559 Using the inverted pendulum model, MacKinnon and Winter found, to make sure balance was preserved, the center of mass should pass medial to the supporting foot.MacKinnon, CD; Winter, DA (1993).

By shining an optical beam on one edge of a liquid droplet, the reduced contact angle creates a pressure difference throughout the droplet, and pushes the droplet's center of mass towards the illuminated side. Control of the optical beam results in control of the droplet's movement. Using 4 mW laser beams, OEW has proven to move droplets of deionized water at speeds of 7mm/s. Traditional electrowetting runs into problems because it requires a two-dimensional array of electrodes for droplet actuation.

This shifts the feet (toes) behind the center of mass of the loon body. They walk usually by pushing themselves on their breasts; larger loons cannot take off from land. This position, however, is highly suitable for swimming because their feet are located at the rear like the propeller on a motorboat. Grebes and many other waterfowl have shorter femur and a more or less narrow pelvis, too, which gives the impression that their legs are attached to the rear as in loons.

For a rigid object in contact with a fixed environment and acted upon by gravity in the vertical direction, its support polygon is a horizontal region over which the center of mass must lie to achieve static stability. For example, for an object resting on a horizontal surface (e.g. a table), the support polygon is the convex hull of its "footprint" on the table. The support polygon succinctly represents the conditions necessary for an object to be at equilibrium under gravity.

A conceptual design for a high-capacity orbiter was drawn up. The concept utilized a series of canisters mounted in the payload bay that would carry 68-74 passengers in a double deck configuration similar to a Boeing 747. This moved the center of mass forward requiring minor changes to the wing structure adding more canard-like surfaces to allow more lifting surface. The design would be used for a Von Braun style space station that would need crew capacity in the hundreds.

This effect is exploited in models of large extra dimensions. The exact value of the grand unification energy (if grand unification is indeed realized in nature) depends on the precise physics present at shorter distance scales not yet explored by experiments. If one assumes the Desert and supersymmetry, it is at around 1016 GeV. The most powerful collider to date, the Large Hadron Collider (LHC), is designed to reach a center of mass energy of 1.4x104 GeV in proton-proton collisions.

Normally, orbit refers to a regularly repeating trajectory, although it may also refer to a non-repeating trajectory. To a close approximation, planets and satellites follow elliptic orbits, with the center of mass being orbited at a focal point of the ellipse,The Space Place :: What's a Barycenter as described by Kepler's laws of planetary motion. For most situations, orbital motion is adequately approximated by Newtonian mechanics, which explains gravity as a force obeying an inverse-square law.Kuhn, The Copernican Revolution, pp.

Another simple approach appropriate for small rockets — or rockets with a large cross-sectional area — is to have the rocket tumble back to earth. Any rocket that will enter a stable, ballistic trajectory as it falls is not safe to use with tumble recovery. To prevent this, some such rockets use the ejection charge to slide the engine to the rear of the rocket, moving the center of mass behind the center of pressure and thus making the rocket unstable.

Wheelies are common in auto- or motorcycle drag racing, where they represent torque wasted lifting the front end, rather than moving the vehicle forward. They also usually result in raising the center of mass, which limits the maximum acceleration. In the absence of wheelie bars, this effect is quantified in the physics section below. If wheelie bars are present then a wheelie results in a reduction of load on the rear driving wheels, along with a corresponding reduction in friction.

More generally, the circumcenter of mass and center of mass coincide for a simplicial polytope for which each face has the sum of squares of its edges a constant. The circumcenter of mass is invariant under the operation of "recutting" of polygons. and the discrete bicycle (Darboux) transformation; in other words, the image of a polygon under these operations has the same circumcenter of mass as the original polygon. The generalized Euler line makes other appearances in the theory of integrable systems.

Kepler-14 is a binary star system targeted by the Kepler spacecraft. It is host to one known planet: the Jupiter-like Kepler-14b. The star system was identified by Kepler as a possible planetary host, but when imaging revealed that Kepler-14 was a binary star system and not a single star, the confirmation process became protracted. The stars are separated by at least 280 AU, and the stars complete an orbit around a common center of mass every 2800 years.

The tensor achieves consistency in part through its standardization of the reference point for gravity. The geocentric system is simpler, being smaller and involving few massive objects: that coordinate system defines its center as the center of mass of the Earth itself. The barycentric system can be loosely thought of as being centered on the Sun, but the Solar System is more complicated. Even the much smaller planets exert gravitational force upon the Sun, causing it to shift position slightly as they orbit.

The BlueZERO concept is based on a single architecture, a sandwich-floor architecture, which allows all of the drive components to be located on this sandwich floor design. This makes it possible to obtain a low center of mass and also leaves ample trunk and interior space. No compromises were made when it comes to passenger space or luggage capacity. With all the major power- train components located between the axles, the BlueZERO achieved a high passenger safety standard commonly associated with Mercedes.

Repeated gravitational interchanges between bodies gradually act to equalize kinetic energy, which is proportional to the square of velocity. The net effect, over sufficiently long times, is sorting by mass. The more massive, low-velocity, objects tend to remain near the center of the cluster, while less massive objects are set on more distant trajectories, or expelled from the system entirely. In any case, the cluster gradually expands, while the most massive objects remain relatively close to the center of mass.

The production of Z bosons through the Drell–Yan process affords the opportunity to study the couplings of the Z boson to quarks. The main observable is the forward–backward asymmetry in the angular distribution of the two leptons in their center-of-mass frame. If heavier neutral gauge bosons exist (see Z' boson), they might be discovered as a peak in the dilepton invariant mass spectrum in much the same way that the standard Z boson appears by virtue of the Drell–Yan process.

With smooth-bore firearms, a spherical shape was optimum because no matter how it was oriented, it presented a uniform front. These unstable bullets tumbled erratically and provided only moderate accuracy; however, the aerodynamic shape changed little for centuries. Generally, bullet shapes are a compromise between aerodynamics, interior ballistic necessities, and terminal ballistics requirements. Another method of stabilization is to place the center of mass of the bullet as far forward as is practical, which is how the Minié ball and the shuttlecock are designed.

When guppies detect a predator, their irises rapidly darken from silver to jet black, which draws predators to attack the guppies' head instead of their body's center of mass. Perhaps counterintuitively, this predator divertive behavior allows guppies to rapidly pivot out of the way as predators lunge where the guppies' head was; this "matador-like" anti-predator behavior was first described in guppies but may be found in other animal species with bright, attention-grabbing coloration located on vital organs, such as epaulette sharks.

The objective of the approach is to gradually accelerate to a maximum controlled speed at takeoff. The most important factor for the distance travelled by an object is its velocity at takeoff – both the speed and angle. Elite jumpers usually leave the ground at an angle of twenty degrees or less; therefore, it is more beneficial for a jumper to focus on the speed component of the jump. The greater the speed at takeoff, the longer the trajectory of the center of mass will be.

The Mozambique Drill,See section on Mozambique. also known as the Failure Drill, or Failure to Stop drill, informally, "two to the body, one to the head," is a close-quarters shooting technique that requires the shooter to fire twice into the torso of a target (known as a double tap or hammered pair to the center of mass), and follow up with a more difficult head shot that, if properly placed, will instantly stop the target if the previous shots failed to do so.

Studies of the teeth also reveal that it preferred different vegetation from the other sauropods of the Morrison, such as Camarasaurus. This may have better allowed the various species of sauropods to exist without competition. Diplodocus (green) and various sauropods in a tripodal posture; The white dots showing the approximate center of mass, as estimated in studies. The flexibility of Diplodocus neck is debated but it should have been able to browse from low levels to about 4 m (13 ft) when on all fours.

The blanks were then transported via ship to REOSC, located south of Paris for final grinding and polishing. One decision made during design to save money was eliminating the two Nasmyth platforms. This makes instruments like high resolution spectrographs and adaptive optics systems much more difficult to construct, due to the size and mass requirement inherent with Cassegrain instruments. A further challenge in designing large instruments is the requirement to have a specific mass and center-of-mass position to maintain the overall balance of the telescope.

The pioneering work related to the microparticle levitation was performed by Artur Ashkin in 1970. He demonstrated optical trapping of dielectric microspheres for the first time, forming an optical levitation system, by using a focused laser beam in air and liquid. This new technology was later named "optical tweezer" and applied in biochemistry and biophysics. Later, significant scientific progress on optically levitated systems was made, for example the cooling of the center of mass motion of a micro- or nanoparticle in the millikelvin regime.

The difficulty is that turning left, accomplished by turning the rear wheel to the right, initially moves the center of mass to the right, and vice versa. This complicates the task of compensating for leans induced by the environment. Examination of the eigenvalues for bicycles with common geometries and mass distributions shows that when moving in reverse, so as to have rear-wheel steering, they are inherently unstable. This does not mean they are unridable, but that the effort to control them is higher.

The pair are orbiting their common center of mass in a circular orbit with a period of only 2.622 days, indicating that they are in a relatively tight orbit. The interaction between the two components of this system appears to be creating emission lines in the spectrum, turning the primary into a Be star. It has a stellar classification of B2 IV, which matches a massive B-type subgiant star. The primary has 8.5 times the mass of the Sun and 6.4 times the Sun's radius.

Kepler-47 is a binary star system located about away from Earth. The binary system is composed of a G-type main sequence star (Kepler-47A) and a red dwarf star (Kepler-47B). The stars orbit each other around their barycenter, or center of mass between them, completing one full orbit every 7.45 days. The stars orbit their barycenter from a distance of about 0.084 AU. The stars have 104% and 35% of the Sun's mass, and 96% and 35% of the Sun's radius, respectively.

Menara is likely the tallest flowering plant in the world as it's taller than the previous record holder, a Mountain ash (Eucalyptus regnans) in Tasmania that may be 100.5 m tall. If not counting its roots, Menara weighs nearly 81,500 kilograms. 95% of this mass is located in the trunk, while 5% comes from the 40 meter-wide crown. The stem is extremely straight, with its center of mass at 28 m above the ground, which is just 0.6 m off from the central vertical axis.

However, the primary market was for civilian self-defense, so its most common use was at close range. Common practice at the time, indeed, was not to aim pistols, but instead to "shoot from the hip", holding the gun low and simply pointing at the target's center of mass. Gunfights often happened at point-blank range. With this use in mind, many pepperboxes, in fact, have smooth-bored barrels, even though rifling had been commonly used for decades by the time of their manufacture.

The change of buoyancy is typically done through the use of a pump that can take in or push out water. The vehicle's pitch can be controlled by changing the center of mass of the vehicle. For Slocum gliders this is done internally by moving the batteries, which are mounted on a screw. Because of their low speed and low-power electronics, the energy required to cycle trim states is far less than for regular AUVs, and gliders can have endurances of months and transoceanic ranges.

FMR layout, the engine is located behind the front axle. In automotive design, a front mid- engine, rear-wheel-drive layout (FMR) is one that places the engine in the front, with the rear wheels of vehicle being driven. In contrast to the front- engine, rear-wheel-drive layout (FR), the engine is pushed back far enough that its center of mass is to the rear of the front axle. This aids in weight distribution and reduces the moment of inertia, improving the vehicle's handling.

The following is a list of centroids of various two-dimensional and three- dimensional objects. The centroid of an object X in n-dimensional space is the intersection of all hyperplanes that divide X into two parts of equal moment about the hyperplane. Informally, it is the "average" of all points of X. For an object of uniform composition, the centroid of a body is also its center of mass. In the case of two-dimensional objects shown below, the hyperplanes are simply lines.

The sum of the particle kinetic energies as calculated by an observer is smallest in the center of momentum frame (again, called the "rest frame" if the system is bound). They will often also interact through one or more of the fundamental forces, giving them a potential energy of interaction, possibly negative. For an isolated massive system, the center of mass moves in a straight line with a steady sub-luminal velocity. Thus, an observer can always be placed to move along with it.

The French coalition of forces amounted to 449,000 men and 1,146 cannons being opposed by the Russian armies combining to muster 153,000 Russians, 938 cannons, and 15,000 Cossacks. The center of mass of French forces focused on Kaunas and the crossings were made by the French Guard, I, II and III corps amounting to some 120,000 at this point of crossing alone. The actual crossings were made in the area of Alexioten where three pontoon bridges were constructed. The sites had been selected by Napoleon in person.

This skier is in the middle of a high- performance turn during a slalom race. The arced shape of the ski can be seen, especially on the outside ski (right side of the image). When making a carving turn, a skier is skiing in dynamic equilibrium, so to balance the centripetal force the skier brings their center of mass to the inside of the turn. This is like a cyclist leaning to the inside of a turn to avoid being thrown off of their bicycle.

Celestial bodies rotating about each other often have elliptic orbits. The special case of circular orbits is an example of a rotation around a fixed axis: this axis is the line through the center of mass perpendicular to the plane of motion. The centripetal force is provided by gravity, see also two-body problem. This usually also applies for a spinning celestial body, so it need not be solid to keep together unless the angular speed is too high in relation to its density.

Star system named DI Cha. While only two stars are apparent, it is actually a quadruple system containing two sets of binary stars. Most multiple-star systems are organized in what is called a hierarchical system: the stars in the system can be divided into two smaller groups, each of which traverses a larger orbit around the system's center of mass. Each of these smaller groups must also be hierarchical, which means that they must be divided into smaller subgroups which themselves are hierarchical, and so on.

Orbits of the HR 6819 hierarchical triple star system: an inner binary with one star (orbit in blue) and a black hole (orbit in red), encircled by another star in a wider orbit (also in blue). In a physical triple star system, each star orbits the center of mass of the system. Usually, two of the stars form a close binary system, and the third orbits this pair at a distance much larger than that of the binary orbit. This arrangement is called hierarchical.

Kepler-16 is an eclipsing binary star system in the constellation of Cygnus that was targeted by the Kepler spacecraft. Both stars are smaller than the Sun; the primary, Kepler-16A, is a K-type main-sequence star and the secondary, Kepler-16B, is an M-type red dwarf. They are separated by 0.22 AU, and complete an orbit around a common center of mass every 41 days. The system is host to one known extrasolar planet in circumbinary orbit: the Saturn-sized Kepler-16b.

The satellite is 1.4 magnitudes dimmer than Huya (HV=5.04), giving a visual absolute magnitude of 6.44 for the satellite. The satellite is relatively large compared to Huya, being slightly larger than half the primary's diameter of . The size ratio of the satellite to the primary is 0.525. The large size ratio is analogous to the Pluto–Charon binary system, in which Pluto's large moon Charon is large and massive enough such that the center of mass (barycenter) is located in the space between Charon and Pluto.

The engines proved heavier than originally expected, and the sweep was added primarily to position the center of lift properly relative to the center of mass. (The original 35° sweep, proposed by Adolf Busemann, was not adopted.)Christopher, John. The Race for Hitler's X-Planes (History Press, The Mill, Gloucestershire, 2013, p.48. On 1 March 1940, instead of moving the wing backward on its mount, the outer wing was re-positioned slightly aft; the trailing edge of the midsection of the wing remained unswept.

The magnetic fields for EMFF are generated by sending current through coils of wire. The interaction between the magnetic dipoles created is easily understood with a far field approximation where the separation distance between two vehicles is large compared to the physical size of the dipole. By controlling the dipoles on various vehicles, attraction, repulsion, and shear forces can be created. Combined with reaction wheels, any desired maneuver can be performed as long as the formation’s center of mass is not required to change.

In aeronautics, the roll moment is the product of an aerodynamic force and the distance between where it is applied and the aircraft's center of mass that tends to cause the aircraft to rotate about its roll axis. The roll axis is usually defined as the longitudinal axis, which runs from the nose to the tail of the aircraft. A roll moment can be the result of wind gusts, control surfaces such as ailerons, or simply by flying at an angle of sideslip. See flight dynamics.

AIP Study p. 104 After the discovery of the J/Ψ in November 1974 demonstrated that interesting physics could be done with an electron-positron collider, Cornell submitted a proposal in 1975 for an electron-positron collider operating up to center-of-mass energies of 16 GeV using the existing synchrotron tunnel. An accelerator at 16 GeV would explore the energy region between that of the SPEAR accelerator and the PEP and PETRA accelerators.Berkelman (2004) p. 19 CESR and CLEO were approved in 1977Berkelman (2004) p.

Gravitational potential energy increases when two objects are brought further apart. For two pairwise interacting point particles, gravitational energy is determined by the masses of the particles, their separation, and the gravitational constant (). Close to the Earth's surface, the gravitational field is approximately constant, and the gravitational potential energy U of an object reduces to :U = mgh where m is the object's mass, g is the gravity of Earth, and h is the height of the object's center of mass above a chosen reference level.

Allosauroids scaled their limbs relative to their body in a way similar to how other large theropods, like the tyrannosaurids, did. During the Cretaceous, some allosauroids grew to sizes similar to those of the largest tyrannosaurids. These large allosauroids lived in the same time period as the other large theropods found in the upper Morrison and Tendaguru formations. Allosauroids maintained a similar center of mass across all sizes, which is found to be between 37% and 58% of the femoral length anterior to the hip.

1959 250 TR59/60 Spider Fantuzzi, showing the tall windshield used on 1960 cars Dry sump lubrication systems became standard equipment for all 250 TRs in 1960. This allowed the engine to sit lower in the chassis, lowering the car's center of mass for improved handling and enabling a lower, more aerodynamic front profile. Rear independent suspension was introduced to the 250 TR in 1960. The car equipped with independent suspension was designated the 250 TRI60 (chassis 0780TR) and throughout the season raced alongside the 250 TR60 equipped with a conventional de Dion rear axle.

Slackwire and tightrope appear to be very similar skills to walking and balancing on a thin wire or rope. In fact, the technique of balance is very different between them. Tightrope performance (Korea) Slackwire and tightwire/tightrope require different balancing techniques: tightrope performers keep their balance by shifting their weight over the rigid tight wire, while slackwire performers use a precise swinging motion to move the relaxed slackwire under their center of mass. Because of this, an artist who works on a tightrope cannot easily make a transition to the slackwire, and vice versa.

In gravitationally bound systems, the orbital speed of an astronomical body or object (e.g. planet, moon, artificial satellite, spacecraft, or star) is the speed at which it orbits around either the barycenter or, if one object is much more massive than the other bodies in the system, its speed relative to the center of mass of the most massive body. The term can be used to refer to either the mean orbital speed, i.e. the average speed over an entire orbit, or its instantaneous speed at a particular point in its orbit.

Unlike axially symmetrical bodies that, if unrestricted, can perform a linear rolling motion (like the sphere or the cylinder) or a circular one (like the cone), developable rollers meander while rolling. Their motion is linear only on average. In the case of the polycons and Platonicons, as well as some of the prime polysphericons, the path of their center of mass consists of circular arcs. In the case of the prime polysphericons that have surfaces that contain cylindrical parts the path is a combination of circular arcs and straight lines.

Used in the method described, even the bâton percés hole can be dispensed with, though the resulting spear thrower would be far more difficult to load and use. The cord used works well when it is long enough that about of cord extends from the hole of the bâton percé to the knot on the spear. Longer cords up to may provide higher velocities. Cord attachment points can vary from the middle of the spear to the center of mass, depending on the length, and a significantly front-heavy spear works best.

He noticed that the shell of an egg usually has many small bumps and dimples so that, by turning the egg in different directions, it can be made to touch a flat surface on three points at the same time in many ways. It is not hard to find an orientation such that the egg's center of mass is contained within the triangle spanned by the three contact points, which is the condition for balancing any object. His findings were replicated by astronomer Frank D. Ghigo of the University of Minnesota in 1984.Schmid, Randolph.

This star system was first catalogued as a binary star by William Herschel in the late 18th century in his study of binary stars. Herschel proved that this system is a gravitationally bound binary system where the two stars orbit around a common center of mass. This was an important contribution to the proof that Newton's law of universal gravitation applied to objects beyond the solar system. He commented at the time that there was a possible third unseen companion affecting the orbit of the two visible stars.

Small size provides many advantages to arboreal species: such as increasing the relative size of branches to the animal, lower center of mass, increased stability, lower mass (allowing movement on smaller branches) and the ability to move through more cluttered habitat. Size relating to weight affects gliding animals such as the sugar glider. Some species of primate, bat and all species of sloth achieve passive stability by hanging beneath the branch. Both pitching and tipping become irrelevant, as the only method of failure would be losing their grip.

The V-hull on the Marine Personnel Carrier (highlighted in green) protects well against IED's but raises the center-of-mass increasing the likelihood of rollovers The V-hull is a type of vehicle armor design used on wheeled armored personnel carriers (APC), infantry mobility vehicles, infantry fighting vehicles (IFV) and MRAPs. The design originated in the 1970s with vehicles such as the iconic Casspir used extensively during the South African Border War, Leopard security vehicle used in the Rhodesian Bush War and South African armored vehicle company Land Systems OMC's and Buffel.

The box to postpone the transmission instead, a system also used in subsequent FJr. it offered a double advantage: making rapid replacement of differential gears that determine the final drive ratio, (allowing a rapid adaptation to the circuit) and, simultaneously, significantly lowering the driveshaft, which in turn governed the position of the driving seat. This allowed a lowering of center of mass with the consequent improvement of handling. The racing debut occurred on July 1954 to the third edition of "Luigi Arcangeli Cup", raced on the Forlì circuit.

Expanding both nucleotides results in a 90% increase in stacking strength. While xG has an overall negative effect on the binding strength of the helix, the other three expanded bases outweigh this with their positive effects. The change in energy caused by expanding the bases is mostly dependent on the rotation of the bond about the nucleobases' centers of mass, and center of mass stacking interactions improve the stacking potential of the helix. Because the size-expanded bases widen the helix, it is more thermally stable with a higher melting temperature.

A central configuration is an initial configuration such that if the particles were all released with zero velocity, they would all collapse toward the center of mass . Such a motion is called homothetic. Central configurations may also give rise to homographic motions in which all masses moves along Keplerian trajectories (elliptical, circular, parabolic, or hyperbolic), with all trajectories having the same eccentricity . For elliptical trajectories, corresponds to homothetic motion and gives a relative equilibrium motion in which the configuration remains an isometry of the initial configuration, as if the configuration was a rigid body.

The paraboloid shape of Archeocyathids produces conic sections on rock faces Conic sections are important in astronomy: the orbits of two massive objects that interact according to Newton's law of universal gravitation are conic sections if their common center of mass is considered to be at rest. If they are bound together, they will both trace out ellipses; if they are moving apart, they will both follow parabolas or hyperbolas. See two-body problem. The reflective properties of the conic sections are used in the design of searchlights, radio-telescopes and some optical telescopes.

Usually this two-body motion is taken to consist of circular orbits around the center of mass, and the planetoid is assumed to move in the plane defined by the circular orbits. The restricted three-body problem is easier to analyze theoretically than the full problem. It is of practical interest as well since it accurately describes many real-world problems, the most important example being the Earth–Moon–Sun system. For these reasons, it has occupied an important role in the historical development of the three-body problem.

The origins of the magnetic field can be explained by the dynamo theory; i.e., by the convection of electrically conductive molten iron in the planet's outer core. A dynamo is generated by a large iron core that has sunk to a planet's center of mass, has not cooled over the years, an outer core that has not been completely solidified, and circulates around the interior. Before the discovery of its magnetic field in 1974, it was thought that because of Mercury's small size, its core had cooled over the years.

A detailed physical modelling-based analysis of sauropod rearing capabilities by Heinrich Mallison showed that while many sauropods could rear, the unusual body shape and limb length ratio of brachiosaurids made them exceptionally ill-suited for rearing. The forward position of its center of mass would have led to problems with stability, and required unreasonably large forces in the hips to obtain an upright posture. Brachiosaurus would also have gained only 33% more feeding height, compared to other sauropods, for which rearing may have tripled the feeding height.Mallison, H. (2011).

A polyatomic molecule (consisting of two or more atoms bound together) can store heat energy in other forms besides its kinetic energy. These forms include rotation of the molecule, and vibration of the atoms relative to its center of mass. These extra degrees of freedom contribute to the molar heat capacity of the substance. Namely, when heat energy is injected into a gas with polyatomic molecules, only part of it will go into increasing their kinetic energy, and hence the temperature; the rest will go to into those other degrees of freedom.

They had calcite guards, and aragonite pro-ostraca and phragmocones, though a few belemnites also had aragonite guards, and the alveolar side of the guards of belemnitellids may have also been of aragonite. The pro-ostracum probably supported the soft parts of the belemnite, similar to the gladius of squid, and completely surrounded the phragmocone. The phragmocone was divided by septa into chambers, much like the shells of cuttlefish and nautiluses. The chambered phragmocone was probably the center of buoyancy, and so was positioned directly above the center of mass for stability purposes.

Proton-Lead ion collision recorded by the ALICE Experiment on 13 September 2012 at a center of mass energy per colliding nucleon-nucleon pair of 5.02 TeV. In 2013, the LHC collided protons with lead ions for the LHC's first physics beams of 2013.First lead-ion collisions in the LHC Symmetry Magazine, 8 November 2010. The experiment was conducted by counter-rotating beams of protons and lead ions, and begun with centred orbits with different revolution frequencies, and then separately ramped to the accelerator's maximum collision energy.

A particle moving inside the Sinai billiard, also known as Lorentz gas. The table of the Lorentz gas (also known as Sinai billiard) is a square with a disk removed from its center; the table is flat, having no curvature. The billiard arises from studying the behavior of two interacting disks bouncing inside a square, reflecting off the boundaries of the square and off each other. By eliminating the center of mass as a configuration variable, the dynamics of two interacting disks reduces to the dynamics in the Sinai billiard.

Qazvin was the location of a former capital of the Persian Empire and contains over 2000 architectural and archeological sites. It is a provincial capital today that has been a cultural center of mass throughout history. Archeological findings in the Qazvin plain reveal the existence of urban agricultural settlements as far back as 7000 BC. The name “Qazvin” or “Kasbin” is derived from Cas, an ancient tribe that lived south of the Caspian Sea millennia ago. The Caspian Sea itself in fact derives its name from the same origin.

Reaction wheels are used to control the attitude of a satellite without the use of thrusters, which reduces the mass fraction needed for fuel. They work by equipping the spacecraft with an electric motor attached to a flywheel, which, when its rotation speed is changed, causes the spacecraft to begin to counter-rotate proportionately through conservation of angular momentum. Reaction wheels can rotate a spacecraft only around its center of mass (see torque); they are not capable of moving the spacecraft from one place to another (see translational force).

Designers therefore supplement reaction wheel systems with other attitude control mechanisms. In the presence of a magnetic field (as in low Earth orbit), a spacecraft can employ magnetorquers (better known as torque rods) to transfer angular momentum to the Earth through its planetary magnetic field. In the absence of a magnetic field, the most efficient practice is to use either high-efficiency attitude jets such as ion thrusters, or small, lightweight solar sails placed in locations away from the spacecraft's center of mass, such as on solar cell arrays or projecting masts.

Dialogue Concerning Two New Sciences (1638) (The Motion of Projectiles: Theorem 1). For objects extended in space, such as a diver jumping from a diving board, the object itself follows a complex motion as it rotates, but the center of mass of the object nevertheless moves along a parabola. As in all cases in the physical world, the trajectory is always an approximation of a parabola. The presence of air resistance, for example, always distorts the shape, although at low speeds, the shape is a good approximation of a parabola.

The third flight of a Luna 8K72 (December 1958), which was to launch the Luna E-1 No.3 probe, ended 245 seconds after launch when the Blok A core stage shut down from loss of engine lubricant. The resonant vibration problem suffered by the 8K72 booster was the cause of a major argument between the Korolev and Glushko design bureaus over the cause and solution to it. It was believed that the vibrations developed as a consequence of adding the Blok E upper stage to the R-7, shifting its center of mass.

Known also as "battle zero", maximum point-blank range is crucial in the military. Soldiers are instructed to fire at any target within this range by simply placing their weapon's sights on the center of mass of the enemy target. Any errors in range estimation are effectively irrelevant, as a well-aimed shot will hit the torso of the enemy soldier. Any height correction is not needed at the "battle zero" or less distance; however, if given, it can result in a headshot or even a complete miss.

ECEF coordinates in relation to latitude and longitude ECEF (acronym for earth-centered, earth-fixed), also known as ECR (initialism for earth-centered rotational), is a geographic and Cartesian coordinate system and is sometimes known as a "conventional terrestrial" system. It represents positions as X, Y, and Z coordinates. The point (0, 0, 0) is defined as the center of mass of Earth, hence the term geocentric coordinates. The distance from a given point of interest to the center of Earth is called the geocentric radius or geocentric distance.

Diagram showing how a smaller object (such as an extrasolar planet) orbiting a larger object (such as a star) could produce changes in position and velocity of the latter as they orbit their common center of mass (red cross). barycenter of solar system relative to the Sun. Apart from the fundamental function of providing astronomers with a reference frame to report their observations in, astrometry is also fundamental for fields like celestial mechanics, stellar dynamics and galactic astronomy. In observational astronomy, astrometric techniques help identify stellar objects by their unique motions.

A particle accelerator is a machine that uses electromagnetic fields to propel charged particles to very high speeds and energies, and to contain them in well-defined beams. Large accelerators are used for basic research in particle physics. The largest accelerator currently operating is the Large Hadron Collider (LHC) near Geneva, Switzerland, operated by the CERN. It is a collider accelerator, which can accelerate two beams of protons to an energy of 6.5 TeV and cause them to collide head-on, creating center-of-mass energies of 13 TeV.

The latest determination of the distance to Maffei 1, which is based on the re-calibrated luminosity/velocity dispersion relation for the elliptical galaxies and the updated extinction, is . The larger (≥3 Mpc) distances reported in the past 20 years would imply that Maffei 1 has never been close enough to the Local Group to significantly influence its dynamics. Maffei 1 moves away from the Sun at the speed of about 66 km/s. Its velocity relative to the Local Group's center of mass is, however, 297 km/s away.

First, the possible sources of bias will be considered. There are three quantities that must be measured: (1) the length of the pendulum, from its suspension point to the center of mass of the “bob;” (2) the period of oscillation; (3) the initial displacement angle. The length is assumed to be fixed in this experiment, and it is to be measured once, although repeated measurements could be made, and the results averaged. The initial displacement angle must be set for each replicate measurement of the period T, and this angle is assumed to be constant.

The suited astronauts are lowered into the pool using an overhead crane and their weight is adjusted by support divers so that they experience no buoyant force and no rotational moment about their center of mass. The suits worn in the NBL are down-rated from fully flight-rated EMU suits like those in use on the space shuttle and International Space Station. The NBL tank is in length, wide, and deep, and contains 6.2 million gallons (23.5 million litres) of water. Divers breathe nitrox while working in the tank.

Antiope orbits in the outer third of the core region of the asteroid belt, and is a member of the Themis family. Since each component is about 86±1 km across, with their centers separated by only about 171 kilometers, the gap separating the two halves is about the same as the diameter of each component. As a result, the two bodies orbit around the common center of mass which lies in the space between them. The orbital period is approximately 16.50 hours, and the eccentricity below 0.006.

Binaries provide the best method for astronomers to determine the mass of a distant star. The gravitational pull between them causes them to orbit around their common center of mass. From the orbital pattern of a visual binary, or the time variation of the spectrum of a spectroscopic binary, the mass of its stars can be determined, for example with the binary mass function. In this way, the relation between a star's appearance (temperature and radius) and its mass can be found, which allows for the determination of the mass of non-binaries.

Each of the three medians of a triangle is a line segment going through one vertex and the midpoint of the opposite side, so it bisects that side (though not in general perpendicularly). The three medians intersect each other at the centroid of the triangle, which is its center of mass if it has uniform density; thus any line through a triangle's centroid and one of its vertices bisects the opposite side. The centroid is twice as close to the midpoint of any one side as it is to the opposite vertex.

Stars of Higher Multiplicity, David S. Evans, Quarterly Journal of the Royal Astronomical Society 9 (1968), 388–400. Each level of the hierarchy can be treated as a two-body problem by considering close pairs as if they were a single star. In these systems there is little interaction between the orbits and the stars' motion will continue to approximate stable Keplerian orbits around the system's center of mass,Dynamics of multiple stars: observations , A. Tokovinin, in "Massive Stars in Interacting Binaries", 16–20 August 2004, Quebec (ASP Conf. Ser., in print).

Because top quarks are very massive, large amounts of energy are needed to create one. The only way to achieve such high energies is through high-energy collisions. These occur naturally in the Earth's upper atmosphere as cosmic rays collide with particles in the air, or can be created in a particle accelerator. In 2011, after the Tevatron ceased operations, the Large Hadron Collider at CERN became the only accelerator that generates a beam of sufficient energy to produce top quarks, with a center-of-mass energy of 7 TeV.

A geonium atom, so named because it is bound to the earth, is a pseudo- atomic system created in a Penning trap, useful for measuring fundamental parameters of particles. In the simplest case, the trapped system consists of only one particle or ion. Such a quantum system is determined by quantum states of one particle, like in the hydrogen atom. Hydrogen consists of two particles, the nucleus and electron, but the electron motion relative to the nucleus is equivalent to one particle in an external field, see center-of-mass frame.

The trim ring, usually black (It may have additional trim colors), that is found directly on top of the hosel on many woods and irons. The ferrule is mostly decorative, creating a continuous line between the shaft and the wider hosel, but in some cases it can form part of the securing mechanism between hosel and shaft. Ferrules of differing weights can fine-tune the center of mass of the overall club head, but for these minute adjustments, screw-in weighted inserts at specific points on the club head are usually used instead.

In geometry, the circumcenter of mass is a center associated with a polygon which shares many of the properties of the center of mass. More generally, the circumcenter of mass may be defined for simplicial polytopes and also in the spherical and hyperbolic geometries. In the special case when the polytope is a quadrilateral or hexagon, the circumcenter of mass has been called the "quasicircumcenter" and has been used to define an Euler line of a quadrilateral.. The circumcenter of mass allows us to define an Euler line for simplicial polytopes.

In the special case when the polygon is cyclic, the circumcenter of mass coincides with the circumcenter. The circumcenter of mass satisfies an analog of Archimedes' Lemma, which states that if a polygon is decomposed into two smaller polygons, then the circumcenter of mass of that polygon is a weighted sum of the circumcenters of mass of the two smaller polygons. As a consequence, any triangulation with nondegenerate triangles may be used to define the circumcenter of mass. For an equilateral polygon, the circumcenter of mass and center of mass coincide.

The aperiodic structures obtained by the cut-and-project method are made diffractive by choosing a suitable orientation for the construction; this is a geometric approach that has also a great appeal for physicists. Classical theory of crystals reduces crystals to point lattices where each point is the center of mass of one of the identical units of the crystal. The structure of crystals can be analyzed by defining an associated group. Quasicrystals, on the other hand, are composed of more than one type of unit, so, instead of lattices, quasilattices must be used.

Due to recent technological advances, a growing trend in balance assessments has become the monitoring of center of pressure (terrestrial locomotion) (CoP), the reaction vector of center of mass on the ground, path length for a specified duration. With quantitative assessments, minimal CoP path length is suggestive of good balance. Laboratory-grade force plates are considered the "gold-standard" of measuring CoP. The NeuroCom Balance Manager (NeuroCom, Clackamas, OR, United States) is a commercially available dynamic posturography system that uses computerized software to track CoP during different tasks.

Monochromatization in the context of accelerator physics is a theoretical principle used to increase center-of-mass energy resolution in high-luminosity particle collisions. The decrease of the collision energy spread can be accomplished without reducing the inherent energy spread of either of the two colliding beams, introducing opposite correlations between spatial position and energy at the interaction point (IP). In beam-optical terms, this can be accomplished through a non-zero dispersion function for both beams of opposite sign at the IP. The dispersion is determined by the respective lattice.

The reason for the 5.3 arcsecond offset between the IERS Reference Meridian and the Airy transit circle is that the observations with the transit circle were based on the local vertical, while the IERS Reference is a geodetic longitude, that is, the plane of the meridian contains the center of mass of the Earth. The International Hydrographic Organization adopted an early version of the IRM in 1983 for all nautical charts. Section 2.4.4. The IRM was adopted for air navigation by the International Civil Aviation Organization on 3 March 1989.

The rear-engine, rear-wheel drive layout (abbreviated as RR layout) places both the engine and drive wheels at the rear of the vehicle. In contrast to the MR layout, the center of mass of the engine is between the rear axle and the rear bumper. Although very common in transit buses and coaches due to the elimination of the drive shaft with low-floor bus, this layout has become increasingly rare in passenger cars. The Porsche 911 is notable for its continuous use of the RR layout since 1963.

The HER and LER are constructed side-by-side in the tunnel, which has been excavated already in the past for the former TRISTAN accelerator. TRISTAN was the first site to confirm vacuum polarization around an electron and operated at center-of-mass energies between 50 and 61.4 GeV. There were four experiments at the old TRISTAN accelerator: Venus, Topaz, AMY, and Jade. The RF cavities in the HER use superconducting RF (SRF) technology, whereas the RF cavities in the LER use a normal conducting design denoted ARES.

Johnson’s work was concentrated on the theoretical particle created in the decays of Higgs boson; specifically in collisions that decay to b-jets and the particle that lives long enough to travel at least 1.6 cm before decaying into heavy quarks. The Higgs Boson is the only Standard Model of particle physics predicted to exist that has not been observed. Johnson’s novel search for the unnamed particle is theorized to arise in the “hidden valley” sector of particle physics. Johnson’s work involved mapping center-of-mass energy of 1.96TeV.

The image collected from each pulse of the lasers is then sent to a computer, and the results of many thousands of laser pulses are accumulated to provide an image such as the one for ozone shown previously. In this position-sensing version of product imaging, the position of the ions as they hit the detector is recorded. One can imagine the ions produced by the dissociation and ionization lasers as expanding outward from the center-of-mass with a particular distribution of velocities. It is this three-dimensional object that we wish to detect.

The cylindrical axis is the axis containing the polarization direction of the dissociating light. It is important to note that the image is taken in the center-of-mass frame; no transformation, other than from time to speed, is needed. A final advantage of the technique should also be mentioned: ions of different masses arrive at the detector at different times. This differential arises because each ion is accelerated to the same total energy, E, as it traverses the electric field, but the acceleration speed, vz, varies as E = ½ mvz2.

CMS is designed as a general-purpose detector, capable of studying many aspects of proton collisions at 0.9–13 TeV, the center-of-mass energy of the LHC particle accelerator. The CMS detector is built around a huge solenoid magnet. This takes the form of a cylindrical coil of superconducting cable that generates a magnetic field of 4 tesla, about 100 000 times that of the Earth. The magnetic field is confined by a steel 'yoke' that forms the bulk of the detector's weight of 12 500 t.

HD 2942 is a triple star system in the constellation Andromeda located approximately away. The primary component, a red giant of spectral type K0III, has an apparent magnitude of 6.33, meaning that it is barely visible with the naked eye under good conditions. The secondary component is much fainter, with an apparent magnitude 11.26, and is located 8.6 arcseconds away. It is a double-lined spectroscopic binary, where two very similar G-type main sequence stars of spectral types G6V and G8V orbit around their common center of mass in 7.489 days.

The nuclear star cluster of our own Milky Way Galaxy seen with adaptive optics in the infrared with the NaCo instrument on the VLT. A nuclear star cluster (NSC) or compact stellar nucleus (sometimes called young stellar nucleus) is a star cluster with high density and high luminosity near the center of mass of most galaxies. NSCs are the central massive objects of fainter, low-mass galaxies where supermassive black holes (SMBHs) are not present or are of negligible mass. In the most massive galaxies, NSCs are entirely absent.

The planet, called Kepler-16b, is about 200 light years from Earth, in the constellation Cygnus, and is believed to be a frozen world of rock and gas, about the mass of Saturn. It orbits two stars that are also circling each other, one about two-thirds the size of our sun, the other about a fifth the size of our sun. Each orbit of the stars by the planet takes 229 days, while the planet orbits the system's center of mass every 225 days; the stars eclipse each other every three weeks or so.

He noted that the tides varied in time and strength in different parts of the world. According to Lucio Russo, Seleucus ascribed tides both to the Moon and to a whirling motion of the Earth, which could be interpreted as the motion of the Earth around the Earth-Moon center of mass. According to Strabo (1.1.9), Seleucus was the first to state that the tides are due to the attraction of the Moon, and that the height of the tides depends on the Moon's position relative to the Sun.

Like the other two exoplanets, HD 40307 b and HD 40307 d, orbiting the star HD 40307, HD 40307 c was discovered by measuring variations in the radial velocity of HD 40307 caused by the star's orbit around the center of mass of the planetary system. These measurements were made by the High Accuracy Radial Velocity Planet Searcher spectrograph apparatus (HARPS) at the La Silla Observatory in Chile's Atacama Desert. The discovery of planets in the HD 40307 system was announced in an astrophysics convention that took place in Nantes, France in mid-June 2008.

Technically escape velocity can either be measured as a relative to the other, central body or relative to center of mass or barycenter of the system of bodies. Thus for systems of two bodies, the term escape velocity can be ambiguous, but it is usually intended to mean the barycentric escape velocity of the less massive body. In gravitational fields, escape velocity refers to the escape velocity of zero mass test particles relative to the barycenter of the masses generating the field. In most situations involving spacecraft the difference is negligible.

ABS sensor ring on a BMW R1200RT There are generally two independent brakes on a motorcycle, one set on the front wheel and one on the rear. However, some models have "linked brakes" whereby both can be applied at the same time using only one control. Front brakes are generally much more effective than rear brakes: roughly two thirds of stopping power comes from the front brake—mainly as a result of weight transfer being much more pronounced compared to longer or lower vehicles, because of the motorcycle's short wheelbase relative to its center of mass height. This can result in brake dive.

This was later established to have been due to a wiring error prior to launch. Engineers developed a solution which involved pressurizing the tank using the pressurization system from the number one tank, which was still working, once the propellant in that tank had been used. When orbit raising operations resumed on 19 March, it was estimated that it would take two months to raise the satellite's orbit. It was later discovered that only using fuel from the number one tank upset the satellite's center of mass, causing the satellite to tumble when its main engines were fired.

Having one wheel in front and two in the rear for power reduces the cost of the steering mechanism but greatly decreases lateral stability when cornering while braking. When the single wheel is in the front (the "delta" form, as in a child's pedal tricycle), the vehicle is inherently unstable in a braking turn, as the combined tipping forces at the center of mass from turning and braking can rapidly extend beyond the triangle formed by the contact patches of the wheels. This type, if not tipped, also has a greater tendency to spin out ("swap ends") when handled roughly.

Examples of the latter design include the Concorde, F-104 Starfighter and XB-70 Valkyrie, although to some degree practically every post-World War II interceptor aircraft featured such a design. Missile designers are even less interested in low-speed performance, and missiles generally have higher fineness ratios than most aircraft. The introduction of aircraft with higher fineness ratios also introduced a new form of instability, inertial coupling. As the engines and cockpit moved away from the aircraft's center of mass, the roll inertia of these masses grew to be able to overwhelm the power of the aerodynamic surfaces.

The Moon is an exceptionally large natural satellite relative to Earth: Its diameter is more than a quarter and its mass is 1/81 of Earth's. It is the largest moon in the Solar System relative to the size of its planet, though Charon is larger relative to the dwarf planet Pluto, at 1/9 Pluto's mass. The Earth and the Moon's barycentre, their common center of mass, is located (about a quarter of Earth's radius) beneath Earth's surface. The Earth revolves around the Earth-Moon barycentre once a sidereal month, with 1/81 the speed of the Moon, or about per second.

Watson-built roadsters won in 1956, 1959 - 1964 though the 1961 and 1963 winners were actually close copies built from Watson designs. The 1957 and 1958 winner was the same car built by Salih with help by Epperly built with a unique placement of the engine in a 'lay down' mounting so the cylinders were nearly horizontal instead of vertical as traditional design dictated. This gave a slightly lower center of mass and a lower profile. Roadsters continued to race until the late 1960s, although they became increasingly uncompetitive against the new rear-engined racing cars.

Hydrodynamic chromatography (HDC) is derived from the observed phenomenon that large droplets move faster than small ones. In a column, this happens because the center of mass of larger droplets is prevented from being as close to the sides of the column as smaller droplets because of their larger overall size. Larger droplets will elute first from the middle of the column while smaller droplets stick to the sides of the column and elute last. This form of chromatography is useful for separating analytes by molar mass, size, shape, and structure when used in conjunction with light scattering detectors, viscometers, and refractometers.

Radius of gyration or gyradius of a body about an axis of rotation is defined as the radial distance to a point which would have a moment of inertia the same as the body's actual distribution of mass, if the total mass of the body were concentrated. Mathematically the radius of gyration is the root mean square distance of the object's parts from either its center of mass or a given axis, depending on the relevant application. It is actually the perpendicular distance from point mass to the axis of rotation. One can represent a trajectory of a moving point as a body.

Thus, the molecules are free to flow and their center of mass positions are randomly distributed as in a liquid, but still maintain their long-range directional order. Most nematics are uniaxial: they have one axis (called directrix) that is longer and preferred, with the other two being equivalent (can be approximated as cylinders or rods). However, some liquid crystals are biaxial nematics, meaning that in addition to orienting their long axis, they also orient along a secondary axis. Nematics have fluidity similar to that of ordinary (isotropic) liquids but they can be easily aligned by an external magnetic or electric field.

As with other glyptodonts and xenarthrans, the center of mass appears to have been closer to the hind limbs than the forelimbs, indicating the vast majority and in some instance nearly all of the weight was borne on the hind limbs. This might show that glyptodonts, when their weight was displaced farther tailwards, could stand on two legs, though not necessarily maintaining an erect posture. Modern xenarthrans commonly stand up in this fashion for defense, to observe, or to feed. Strong hind limbs would also have been important while accelerating the tail club and maintaining posture after getting hit.

The total torque exerted by the triangle is its area, 1/2, times the distance 2/3 of its center of mass from the fulcrum at x = 0\. This torque of 1/3 balances the parabola, which is at a distance -1 from the fulcrum. Hence, the area of the parabola must be 1/3 to give it the opposite torque. This type of method can be used to find the area of an arbitrary section of a parabola, and similar arguments can be used to find the integral of any power of x, although higher powers become complicated without algebra.

At RHIC the programme began with four experiments— PHENIX, STAR, PHOBOS, and BRAHMS—all dedicated to study collisions of highly relativistic nuclei. Unlike fixed-target experiments, collider experiments steer two accelerated beams of ions toward each other at (in the case of RHIC) six interaction regions. At RHIC, ions can be accelerated (depending on the ion size) from 100 GeV/nucleon to 250 GeV/nucleon. Since each colliding ion possesses this energy moving in opposite directions, the maximal energy of the collisions can achieve a center-of-mass collision energy of 200 GeV/nucleon for gold and 500 GeV/nucleon for protons.

While many of the ideas of calculus had been developed earlier in Greece, China, India, Iraq, Persia, and Japan, the use of calculus began in Europe, during the 17th century, when Isaac Newton and Gottfried Wilhelm Leibniz built on the work of earlier mathematicians to introduce its basic principles. The development of calculus was built on earlier concepts of instantaneous motion and area underneath curves. Applications of differential calculus include computations involving velocity and acceleration, the slope of a curve, and optimization. Applications of integral calculus include computations involving area, volume, arc length, center of mass, work, and pressure.

However, studies have shown that the center of mass of Diplodocus was very close to the hip socket; this means that Diplodocus could rear up into a bipedal posture with relatively little effort. It also had the advantage of using its large tail as a 'prop' which would allow for a very stable tripodal posture. In a tripodal posture Diplodocus could potentially increase its feeding height up to about . The neck's range of movement would have also allowed the head to graze below the level of the body, leading some scientists to speculate on whether Diplodocus grazed on submerged water plants, from riverbanks.

Cetacean flippers may be viewed as being analogous to modern engineered hydrofoils, which have hydrodynamic properties: lift coefficient, drag coefficient and efficiency. Flippers are one of the principal control surfaces of cetaceans (whales, dolphins and porpoises) due to their position in front of the center of mass, and their mobility which provides three degrees of freedom. tubercles on the flippers of humpback whales improve the hydrodynamics of the flipper at their size. Breaking up channels of fast- moving water allows humpbacks to retain their “grip” on the water, and turn at sharper angles even at low velocities.

The guided entry is the phase that allowed the spacecraft to steer with accuracy to its planned landing site Precision guided entry made use of onboard computing ability to steer itself toward the pre-determined landing site, improving landing accuracy from a range of hundreds of kilometers to . This capability helped remove some of the uncertainties of landing hazards that might be present in larger landing ellipses. Steering was achieved by the combined use of thrusters and ejectable balance masses. The ejectable balance masses shift the capsule center of mass enabling generation of a lift vector during the atmospheric phase.

Ten seconds after peak heating, that deceleration peaked out at 15 g. Much of the reduction of the landing precision error was accomplished by an entry guidance algorithm, derived from the algorithm used for guidance of the Apollo Command Modules returning to Earth in the Apollo program. This guidance uses the lifting force experienced by the aeroshell to "fly out" any detected error in range and thereby arrive at the targeted landing site. In order for the aeroshell to have lift, its center of mass is offset from the axial centerline that results in an off-center trim angle in atmospheric flight.

Countersteering is used by single-track vehicle operators, such as cyclists and motorcyclists, to initiate a turn toward a given direction by momentarily steering counter to the desired direction ("steer left to turn right"). To negotiate a turn successfully, the combined center of mass of the rider and the single-track vehicle must first be leaned in the direction of the turn, and steering briefly in the opposite direction causes that lean. The rider's action of countersteering is sometimes referred to as "giving a steering command". The scientific literature does not provide a clear and comprehensive definition of countersteering.

They are only mobile when connected to the correct tractor unit, which can limit their use in recovery. The simplest semi-trailer is "half of a trailer", having wheels at the rear only and an articulated connection to the tractor unit. A strong metal post or kingpin on the trailer fits into a socket or fifth wheel on the tractor. Lowboy semi-trailers are commonly used to keep the load's center of mass low, as they have a low horizontal bed, with a gooseneck that rises up at the front to connect to the tractor unit.

Mass over the rear wheel can be more easily controlled if it is lower than mass over the front wheel. A bike is also an example of an inverted pendulum. Just as a broomstick is more easily balanced in the hand than a pencil, a tall bike (with a high center of mass) can be easier to balance when ridden than a low one because the tall bike's lean rate (rate at which its angle of lean increases as it begins to fall over) will be slower. However, a rider can have the opposite impression of a bike when it is stationary.

Another factor that can also contribute to the self-stability of traditional bike designs is the distribution of mass in the steering mechanism, which includes the front wheel, the fork, and the handlebar. If the center of mass for the steering mechanism is in front of the steering axis, then the pull of gravity will also cause the front wheel to steer in the direction of a lean. This can be seen by leaning a stationary bike to one side. The front wheel will usually also steer to that side independent of any interaction with the ground.

For example, see An algorithm for generating the Jacobi coordinates for N bodies may be based upon binary trees. In words, the algorithm is described as follows: > Let mj and mk be the masses of two bodies that are replaced by a new body of > virtual mass M = mj \+ mk. The position coordinates xj and xk are replaced > by their relative position rjk = xj − xk and by the vector to their center > of mass Rjk = (mj qj \+ mkqk)/(mj \+ mk). The node in the binary tree > corresponding to the virtual body has mj as its right child and mk as its > left child.

To prevent this heat from reaching interior structures, capsules are typically equipped with an ablative heat shield that melts and then vaporizes, removing the heat. The Apollo command module reentered with the center of mass offset from the center line; this caused the capsule to assume an angled attitude through the air, providing lift that could be used for directional control. Reaction control system thrusters were used to steer the capsule by rotating the lift vector. Parachutes are used for the final descent, sometimes augmented by braking rockets if the capsule is designed to land on the Earth's surface.

If the body shown in the illustration is a homogeneous disc, this moment of inertia is \scriptstyle I=m r^2 /2 . If the disc has the mass 0,5 kg and the radius 0,8 m, the moment of inertia is 0,16 kgm2. If the amount of force is 2 N, and the lever arm 0,6 m, the amount of torque is 1,2 Nm. At the instant shown, the force gives to the disc the angular acceleration α = /I = 7,5 rad/s2, and to its center of mass it gives the linear acceleration a = F/m = 4 m/s2.

With unarticulated wheels, climbing obstacles will cause the body of a vehicle to tilt. If the vehicle's center of mass moves outside of the wheelbase or axle track, the vehicle becomes statically unstable, and will tend to tip over. At speed, a vehicle can become dynamically unstable – that is, it can be tipped over by an obstacle smaller than its static stability limit, or by excessive acceleration or tight turning. Suspension systems often mitigate the tendency of wheeled vehicles to overturn, but unlike fully articulated limbs, they do not provide any ability to recover from an overturned position.

At first glance the top's inversion may mistakenly seem to be a situation where the object spontaneously gains overall energy. This is because the inversion of the top raises the object's center of mass, which means the potential energy has in fact increased. What causes the inversion (and the increase in potential energy) is a torque due to surface friction, which also decreases the kinetic energy of the top, so the total energy does not actually increase. Once the top is spinning on its stem, it does not spin in the opposite direction to which its spin was initiated.

Gemini Orbit Attitude and Maneuvering System, and Reentry (mislabeled "Reaction") Control System The Mercury space capsule and Gemini reentry module both used groupings of nozzles to provide attitude control. The thrusters were located off their center of mass, thus providing a torque to rotate the capsule. The Gemini capsule was also capable of adjusting its reentry course by rolling, which directed its off-center lifting force. The Mercury thrusters used a hydrogen peroxide monopropellant which turned to steam when forced through a tungsten screen, and the Gemini thrusters used hypergolic mono-methyl hydrazine fuel oxidized with nitrogen tetroxide.

In 2010, Gregory S. Paul estimated the weight of a Kentrosaurus at . An estimate for the 4.5 m long composite mount in the Museum für Naturkunde Berlin by Mallison, on the basis of a virtual 3D skeleton and 3D model, varied between 1073 L and 1267 L, and a body mass between , depending on the amount of musculature reconstructed for the tail. The long tail of Kentrosaurus results in a position of the center of mass that is unusually far back for a quadrupedal animal. It rests just in front of the hip, a position usually seen in bipedal dinosaurs.

Bobo doll experiment The Bobo doll experiment (or experiments) is the collective name for the experiments performed by influential psychologist, Albert Bandura. During 1961 and 1963 he studied children's behavior after they watched a human adult model act aggressively towards a Bobo doll, a doll-like toy with a rounded bottom and low center of mass that rocks back to an upright position after it has been knocked down. There are different variations of the experiment. The most notable experiment measured the children's behavior after seeing the human model get rewarded, get punished, or experience no consequence for physically abusing the Bobo doll.

But for objects at such high eccentricity, the Sun's barycentric coordinates are more stable than heliocentric coordinates. The orbit of a long-period comet is properly obtained when the osculating orbit is computed at an epoch after leaving the planetary region and is calculated with respect to the center of mass of the Solar System. Using JPL Horizons, the barycentric orbital elements for epoch 1 January 2050 generate a hyperbolic solution. On its closest approach, Comet ISON passed about from Mars on 1 October 2013, and the remnants of Comet ISON passed about from Earth on 26 December 2013.

The "point-blank range" battle zero setting "П" on the 7.62×39mm AKM rear tangent sight element corresponds to a zero. For the AKM combined with service cartridges the 300 m battle zero setting limits the apparent "bullet rise" within approximately relative to the line of sight. Soldiers are instructed to fire at any target within this range by simply placing the sights on the center of mass (the belt buckle, according to Russian and former Soviet doctrine) of the enemy target. Any errors in range estimation are tactically irrelevant, as a well-aimed shot will hit the torso of the enemy soldier.

The compact object and blue supergiant star form a binary system in which they orbit around their center of mass every 5.599829 days. From the perspective of the Earth, the compact object never goes behind the other star; in other words, the system does not eclipse. However, the inclination of the orbital plane to the line of sight from the Earth remains uncertain, with predictions ranging from 27–65°. A 2007 study estimated the inclination is , which would mean that the semi-major axis is about , or 20% of the distance from the Earth to the Sun.

These advantages do however come at the cost of raising the centre of mass as a result of the higher placement of turrets, thus decreasing the metacentric height. This decrease in stability may cause issues if not corrected by compromises elsewhere to keep the center of mass low. Because of this, superfiring arrangements, while common, are not used exclusively. Examples of non-superfiring designs include but are not limited to the Gangut, Imperatritsa Mariya, and Imperator Nikolai classes of battleships built for the Imperial Russian navy, as well as modern ships such as the Zumwalt-class destroyers.

Elementary particles possess an intrinsic quantum mechanical property known as spin. This is analogous to the angular momentum of an object that is spinning around its center of mass, although strictly speaking these particles are believed to be point-like and cannot be said to be rotating. Spin is measured in units of the reduced Planck constant (ħ), with electrons, protons and neutrons all having spin ½ ħ, or "spin-½". In an atom, electrons in motion around the nucleus possess orbital angular momentum in addition to their spin, while the nucleus itself possesses angular momentum due to its nuclear spin.

Flight control surfaces enable the pilot to control an aircraft's flight attitude and are usually part of the wing or mounted on, or integral with, the associated stabilizing surface. Their development was a critical advance in the history of aircraft, which had until that point been uncontrollable in flight. Aerospace engineers develop control systems for a vehicle's orientation (attitude) about its center of mass. The control systems include actuators, which exert forces in various directions, and generate rotational forces or moments about the aerodynamic center of the aircraft, and thus rotate the aircraft in pitch, roll, or yaw.

The TW Andromedae system is made of two stars in a circular orbit around their center of mass, with an orbital plane almost parallel to our line of sight. The presence of a third body in the system, with a minimum mass of 0.27 and an orbital period of 49.6 years, has been proposed to account for the observed changes in the period of the variability. The radius of the two stars can be measured by looking at the eclipses. Beside that, little is known about the single stars, apart from their spectral types F0 and K0.

The "point-blank range" battle zero setting "П" standing for постоянная (constant) on the 7.62×39mm AK-47 rear tangent sight element corresponds to a zero. These settings mirror the Mosin–Nagant and SKS rifles, which the AK-47 replaced. For the AK-47 combined with service cartridges, the 300 m battle zero setting limits the apparent "bullet rise" within approximately relative to the line of sight. Soldiers are instructed to fire at any target within this range by simply placing the sights on the center of mass (the belt buckle, according to Russian and former Soviet doctrine) of the enemy target.

The snout and other parts of the skull also sported numerous foramina. According to the 2017 study which described D. horneri, scaly integument as well as tactile sensitivity was correlated with the multiple rows of neurovascular foramina seen in crocodylians and tyrannosaurids. The skull was perched at the end of a thick, S-shaped neck, and a long, heavy tail acted as a counterweight to balance out the head and torso, with the center of mass over the hips. Tyrannosaurids are known for their proportionately very small two-fingered forelimbs, although remnants of a vestigial third digit are sometimes found.

Individuals with muscular weakness, occult instability, and decreased postural control are more susceptible to injury than those with better postural control. Instability leads to an increase in postural sway, the measurement of the time and distance a subject spends away from an ideal center of pressure. The measurement of a subject's postural sway can be calculated through testing center of pressure (CoP), which is defined as the vertical projection of center of mass on the ground. Investigators have theorized that if injuries to joints cause deafferentation, the interruption of sensory nerve fibers, and functional instability, then a subject's postural sway should be altered.

The summit of Chimborazo, the point on the Earth's surface that is farthest from the Earth's center The shape of Earth is nearly spherical. There is a small flattening at the poles and bulging around the equator due to Earth's rotation. To second order, Earth is approximately an oblate spheroid, whose equatorial diameter is larger than the pole-to-pole diameter, although the variation is less than 1% of the average radius of the Earth. The point on the surface farthest from Earth's center of mass is the summit of the equatorial Chimborazo volcano in Ecuador ().

Pitch Yaw Roll The upward tilt of the wings and tailplane of an aircraft, as seen on this Boeing 737, is called dihedral angle Flight dynamics is the science of air and space vehicle orientation and control in three dimensions. The three critical flight dynamics parameters are the angles of rotation in three dimensions about the vehicle's center of mass, known as pitch, roll and yaw (See Tait-Bryan rotations for an explanation). The control of these dimensions can involve a horizontal stabilizer (i.e. "a tail"), ailerons and other movable aerodynamic devices which control angular stability i.e.

An object with angular momentum of can be reduced to zero rotation (all of the rotational energy can be transferred out of it) by an angular impulse of or equivalently, by torque or work of for one second, or energy of for one second. The plane perpendicular to the axis of angular momentum and passing through the center of mass, p. 97 is sometimes called the invariable plane, because the direction of the axis remains fixed if only the interactions of the bodies within the system, free from outside influences, are considered. One such plane is the invariable plane of the Solar System.

Jet damping or thrust damping is the effect of rocket exhaust removing energy from the transverse angular motion of a rocket. If a rocket has pitch or yaw motion then the exhaust must be accelerated laterally as it flows down the exhaust tube and nozzle. Once the exhaust leaves the nozzle this lateral momentum is lost to the vehicle and thus serves to damp the lateral oscillations. The jet damping is stabilizing as long as the distance from the instantaneous spacecraft center of mass to the nozzle exit plane exceeds the instantaneous transverse radius of gyration.

C/2000 W1 (Utsunomiya-Jones) is a long-period comet discovered on November 18, 2000, by Syogo Utsunomiya and Albert F. A. L. Jones. The comet has an observation arc of 58 days allowing a reasonable estimate of the orbit. But the near-parabolic trajectory with an osculating perihelion eccentricity of 0.9999996 generates an extreme unperturbed aphelion distance of 2,034,048 AU (32 light-years). The orbit of a long-period comet is properly obtained when the osculating orbit is computed at an epoch after leaving the planetary region and is calculated with respect to the center of mass of the solar system.

For equal masses, one possible central configuration places the masses at the vertices of a regular polygon (forming a Klemperer rosette), a Platonic solid, or a regular polytope in higher dimensions. The centrality of the configuration follows from its symmetry. It is also possible to place an additional point, of arbitrary mass, at the center of mass of the system without changing its centrality. Placing three masses in an equilateral triangle, four at the vertices of a regular tetrahedron, or more generally masses at the vertices of a regular simplex produces a central configuration even when the masses are not equal.

The Western roll was a competitive high jump style for a long time because it was easy to learn and more efficient (allowing clearance of a bar that is closer to the height of the center of mass) than all but the most contorted variants of the scissors. It also enabled a comfortable landing in the crude sand pits provided for high jumpers up until the 1950s. However, the technique is less efficient than the straddle technique, a style that evolved from the Western roll when the rotation of the body was increased to the point where the bar was crossed face down.

The tidal force produced by a massive object (Moon, hereafter) on a small particle located on or in an extensive body (Earth, hereafter) is the vector difference between the gravitational force exerted by the Moon on the particle, and the gravitational force that would be exerted on the particle if it were located at the Earth's center of mass. Whereas the gravitational force subjected by a celestial body on Earth varies inversely as the square of its distance to the Earth, the maximal tidal force varies inversely as, approximately, the cube of this distance.Young, C.A. (1889). A Textbook of General Astronomy p. 288.

The centers of the in- and excircles form an orthocentric system. The intersection of the medians is the centroid. A median of a triangle is a straight line through a vertex and the midpoint of the opposite side, and divides the triangle into two equal areas. The three medians intersect in a single point, the triangle's centroid or geometric barycenter, usually denoted by G. The centroid of a rigid triangular object (cut out of a thin sheet of uniform density) is also its center of mass: the object can be balanced on its centroid in a uniform gravitational field.

Raising a vehicle off of the ground by such a degree raises the center of mass to a point where rolling the vehicle becomes a distinct possibility. The suspension modifications required are often meant for trucks and larger vehicles (unless specialized). If the vehicle's brakes have not been upgraded to compensate for the significant increase in wheel diameter, its braking ability will be greatly diminished. In turning too fast, the weight of the vehicle may shift to extremes that were never considered for the vehicle in question, and may cause loss of traction or damage to the vehicle itself.

These are detected when they reach a scintillator in the scanning device, creating a burst of light which is detected by photomultiplier tubes or silicon avalanche photodiodes (Si APD). The technique depends on simultaneous or coincident detection of the pair of photons moving in approximately opposite directions (they would be exactly opposite in their center of mass frame, but the scanner has no way to know this, and so has a built-in slight direction-error tolerance). Photons that do not arrive in temporal "pairs" (i.e. within a timing-window of a few nanoseconds) are ignored.

For a molecule with atoms, the positions of all nuclei depend on a total of 3 coordinates, so that the molecule has 3 degrees of freedom including translation, rotation and vibration. Translation corresponds to movement of the center of mass whose position can be described by 3 cartesian coordinates. A nonlinear molecule can rotate about any of three mutually perpendicular axes and therefore has 3 rotational degrees of freedom. For a linear molecule, rotation about the molecular axis does not involve movement of any atomic nucleus, so there are only 2 rotational degrees of freedom which can vary the atomic coordinates.

During training exercises, neutral-buoyancy diving is used to simulate the weightlessness of space travel. To achieve this effect, suited astronauts or pieces of equipment are lowered into the pool using an overhead crane and then weighted in the water by support divers so that they experience minimal buoyant force and minimal rotational moment about their center of mass. The suits worn by trainees in the NBL are down-rated from fully flight-rated EMU suits like those in use on the Space Shuttle and International Space Station. Divers breathe nitrox while working in the tank.

It is the first recorded Miocene great ape to have had the diaphragm located in the lower chest cavity, as in Homo, indicating an extended lower back and a greater number of functional lumbar vertebrae. This may have caused lordosis (the normal curvature of the human spine) and moved the center of mass over the hips and legs, which implies some habitual bipedal activity. The robust finger and hypertrophied wrist and elbow bones indicate a strong grip and load bearing adaptations for the arms. The legs also show adaptations for load-bearing, especially at the hypertrophied knee joint.

Triangle , its medial triangle, the Spieker circle (the incircle of the medial triangle), and the Spieker center (the center of the Spieker circle) In geometry, the incircle of the medial triangle of a triangle is the Spieker circle, named after 19th-century German geometer Theodor Spieker. Its center, the Spieker center, in addition to being the incenter of the medial triangle, is the center of mass of the uniform-density boundary of triangle. The Spieker center is also the point where all three cleavers of the triangle (perimeter bisectors with an endpoint at a side's midpoint) intersect each other.

P. 63 in Godefroit, P. and Lambert, O. (eds), Tribute to Charles Darwin and Bernissart Iguanodons: New Perspectives on Vertebrate Evolution and Early Cretaceous Ecosystems. Brussels. Diplodocids, on the other hand, appear to have been well adapted for rearing up into a tripodal stance. Diplodocids had a center of mass directly over the hips, giving them greater balance on two legs. Diplodocids also had the most mobile necks of sauropods, a well-muscled pelvic girdle, and tail vertebrae with a specialised shape that would allow the tail to bear weight at the point it touched the ground.

Estimates of the combined stellar classification for this system range from F5III to F6IV, with the luminosity class of 'IV' or 'III' indicating the primary component is a subgiant or giant star, respectively. It is a member of a close binary system—a spectroscopic binary—whose components complete an orbit about their center of mass once every 1.736 days. Because the primary star is rotating rapidly, it has assumed the shape of an oblate spheroid. The ellipsoidal profile of the star, as viewed from Earth, varies over the course of an orbit causing the luminosity to vary in magnitude during the same period.

Delta Trianguli A is a main sequence star with a stellar classification of G0V and a mass similar to the Sun. The spectral characteristics of the smaller companion Delta Trianguli B are not well determined since the close orbit makes observations difficult, with estimates of the spectral class ranging from G9V to K4V. The Delta Trianguli stars orbit their center of mass with an estimated separation of 0.106 AU; it is certainly less than one AU. The orbital period is 10.02 days and the eccentricity of the orbit is only 0.020. The orbit is inclined about 167° to humans' line of sight.

The stability of a rock structure depends on the location of each rock's center of mass in relation to its support points. If other rocks are also on top or contacting it at any point, then the forces (due to weight) of other rocks also play a role. For an individual rock to be stable, it usually requires at least three contact points to rest on, forming a "tripod." Generally, the closer together the points in the tripod, the less stable the rock will be (thus making it more precarious, and becoming a rock balance sculpture - and many would argue more beautiful).

Derivation of the formula for motion along the Equator. A convenient coordinate system in this situation is the inertial coordinate system that is co-moving with the center of mass of the Earth. Then the following is valid: objects that are at rest on the surface of the Earth, co-rotating with the Earth, are circling the Earth's axis, so they are in centripetal acceleration with respect to that inertial coordinate system. What is sought is the difference in centripetal acceleration of the surveying airship between being stationary with respect to the Earth and having a velocity with respect to the Earth.

As the mysterious pull exceeds one Earth gravity, Shaeffer accelerates the Skydiver to compensate for the unknown X-force until he is in free fall (though the accelerometer registers 1.2 gees). Shaeffer eventually realizes what the X-force is: the tidal force. The strong tidal pull of the neutron star is trying to force the ends of the ship (and Shaeffer himself) into two separate orbits. Shaeffer programs the autopilot in a thrust pattern that allows him to reach the center of mass of the ship in effective free-fall, though he nearly fails to do so.

The Chaplygin sleigh is a simple pedagogical example of a nonholonomic system in mechanics, described by Sergey Chaplygin. It consists of a body that slides frictionlessly on a horizontal plane, with a knife edge that constrains its motion so that the knife slides only longitudinally. Because this constraint is nonholonomic, Liouville's theorem does not apply, and although energy is conserved, the motion is dissipative in the sense that phase-space volume is not conserved. The motion is attracted to an equilibrium, in which the sleigh moves without rotation, with the knife edge trailing the center of mass.

A spacecraft traveling from Earth to Mars via this method will arrive near Mars orbit in approximately 8.5 months, but because the orbital velocity is greater when closer to the center of mass (i.e. the Sun) and slower when farther from the center, the spacecraft will be traveling quite slowly and a small application of thrust is all that is needed to put it into a circular orbit around Mars. If the manoeuver is timed properly, Mars will be "arriving" under the spacecraft when this happens. The Hohmann transfer applies to any two orbits, not just those with planets involved.

A configuration of two wheels in the front and one wheel at the back presents two advantages: it has improved aerodynamics, and that it readily enables the use of a small lightweight motorcycle powerplant and rear wheel. This approach was used by the Messerschmitt KR200 and BMW Isetta. Alternatively, a more conventional front- engine, front wheel drive layout as is common in four-wheeled cars can be used, with subsequent advantages for transversal stability (the center of mass is further to the front) and traction (two driven wheels instead of one). Some vehicles have a front engine driving the single rear wheel, similar to the rear engine driving the rear wheel.

The wheel must support acceleration loads as well as lateral forces when in a turn, and loss of traction can be a challenge. A new tadpole configuration has been proposed with a rear engine driving the front wheels. This concept (Dragonfly Three Wheeler) claims both stability and traction (two driven wheels), as well as a unique driving experience. With two wheels in the front (the "tadpole" form or "reverse trike") the vehicle is far more stable in braking turns, but remains more prone to overturning in normal turns compared to an equivalent four-wheeled vehicle, unless the center of mass is lower and/or further forward.

The Hagedorn theory was able to describe correctly the experimental data from collision with center-of-mass energies up to approximately 10 GeV, but above this region it failed. In 2000 I. Bediaga, E. M. F. Curado and J. M. de Miranda proposed a phenomenological generalization of Hagedorn's theory by replacing the exponential function that appears in the partition function by the q-exponential function from the Tsallis non- extensive statistics. With this modification the generalized theory was able again to describe the extended experimental data. In 2012 A. Deppman proposed a non-extensive self-consistent thermodynamical theory that includes the self- consistency principle and the non-extensive statistics.

Both satellite systems are large and diverse. In fact all of the giant planets of the Solar System possess large satellite systems as well as planetary rings, and it is inferred that this is a general pattern. Several objects farther from the Sun also have satellite systems consisting of multiple moons, including the complex Plutonian system where multiple objects orbit a common center of mass, as well as many asteroids and plutinos. Apart from the Earth-Moon system and Mars' system of two tiny natural satellites, the other terrestrial planets are generally not considered satellite systems, although some have been orbited by artificial satellites originating from Earth.

Follow through and overlapping action: the galloping race horse's mane and tail follow the body. Sequence of photos taken by Eadweard Muybridge. Follow through and overlapping action is a general heading for two closely related techniques which help to render movement more realistically, and help to give the impression that characters follow the laws of physics, including the principle of inertia. "Follow through" means that loosely tied parts of a body should continue moving after the character has stopped and the parts should keep moving beyond the point where the character stopped only to be subsequently "pulled back" towards the center of mass or exhibiting various degrees of oscillation damping.

The container may even be subjected to a force which gives it an overall velocity, or else (equivalently) it may be viewed from an inertial frame in which it has an overall velocity (that is, technically, a frame in which its center of mass has a velocity). In this case, its total relativistic mass and energy increase. However, in such a situation, although the container's total relativistic energy and total momenta increase, these energy and momentum increases subtract out in the invariant mass definition, so that the moving container's invariant mass will be calculated as the same value as if it were measured at rest, on a scale.

While the KMX Kart stunt trike with this setup allows the rear brake to be operated separately, letting the rider do "bootlegger turns", the standard setup for most trikes has the front brake for each side operated by each hand. The center-of-mass of most tadpole trikes is close to the front wheels, making the rear brake less useful. The rear brake may instead be connected to a latching brake lever for use as a parking brake when stopped on a hill. Recumbent trikes often brake one wheel with each hand, allowing the rider to brake one side alone to pull the trike in that direction.

Floating Power was a technology developed in the 1920s by the United States automobile firm of Chrysler, credited mostly to the engineering of Owen Ray Skelton. It was a new means of attaching an engine to its chassis, with the intention of reducing vibration. Four-cylinder engines of the day started and rode rather roughly, transmitting the torque to the whole chassis. By attaching the engine at only two points ("fore-and-aft"), on two points defining an axis that passes through the engine's center of mass, the engine would be able to rotate slightly about this axis and reduce the transmission of torsional vibration to the chassis.

Stride length, body kinematics, kinetics, and elastic energy are biomechanical factors associated with improved running economy. The natural stride length of a trained athlete is related to a better running economy rather than any specific adjustments. Body kinematics encompass a variety of movement parameters associated with a better running economy. A runner with a better running economy has a relatively low amplitude of their center of mass, increased swing of the lower legs during a stride (decreased angle of the back of their knee), and increased angular velocity of plantar flexion during push- off, but has a reduced range of movement during plantar flexion.

Scale model of the Apollo command and service module at the Euro Space Center in Belgium alt= The components of the ELS were housed around the forward docking tunnel. The forward compartment was separated from the central by a bulkhead and was divided into four 90-degree wedges. The ELS consisted of two drogue parachutes with mortars, three main parachutes, three pilot parachutes to deploy the mains, three inflation bags for uprighting the capsule if necessary, a sea recovery cable, a dye marker, and a swimmer umbilical. The command module's center of mass was offset a foot or so from the center of pressure (along the symmetry axis).

It flew a lifting entry with a hypersonic trim angle of attack of −27° (0° is blunt-end first) to yield an average L/D (lift- to-drag ratio) of 0.368.Hillje, Ernest R., "Entry Aerodynamics at Lunar Return Conditions Obtained from the Flight of Apollo 4 (AS-501)," NASA TN D-5399, (1969). The resultant lift achieved a measure of cross-range control by offsetting the vehicle's center of mass from its axis of symmetry, allowing the lift force to be directed left or right by rolling the capsule on its longitudinal axis. Other examples of the spherical section geometry in manned capsules are Soyuz/Zond, Gemini, and Mercury.

The work was originally thought to be lost, but in 1906 was rediscovered in the celebrated Archimedes Palimpsest. The palimpsest includes Archimedes' account of the "mechanical method", so-called because it relies on the law of the lever, which was first demonstrated by Archimedes, and of the center of mass (or centroid), which he had found for many special shapes. Archimedes did not admit the method of indivisibles as part of rigorous mathematics, and therefore did not publish his method in the formal treatises that contain the results. In these treatises, he proves the same theorems by exhaustion, finding rigorous upper and lower bounds which both converge to the answer required.

Also, the struts that hold the centered payload are differentially heated; such causes one of the struts to become longer than the cooler struts and thereby changing the center of mass relative to the center of pressure of the kite. Further, to cause an attitude change, tiny photo thrusters (heated wire) tweak the attitude of the kite; such thrusters do not propel the kite, but are only used to change the attitude of the kite's sail. These mechanisms aim to give authoritative control at minimum power use for giving direction to the kite. Working solar kite groups are considering at least seventeen means of control of the solar kite/solar sail.

A special case of the geosynchronous orbit, the geostationary orbit, has an eccentrity of zero (meaning the orbit is circular), and an inclination of zero in the Earth-Centered, Earth-Fixed coordinate system (meaning the orbital plane is not tilted relative to the Earth's equator). The "ground track" in this case consists of a single point on the Earth's equator, above which the satellite sits at all times. Note that the satellite is still orbiting the Earth — its apparent lack of motion is due to the fact that the Earth is rotating about its own center of mass at the same rate as the satellite is orbiting.

The direction of the push is therefore outwards (rightwards) from the center of mass. When the pushing leg reaches full extension, the left (now support) leg is set down and used to glide, while the right leg lifts and is brought back behind and underneath the skater (recovery) ready to be placed on the ground (set down) and become the new support leg. Once the pushing leg has been recovered, the support leg pushes out in the other direction and the cycle repeats. Note that the pushes are always in a lateral direction: the left leg pushes exclusively leftwards, and the right leg exclusively rightwards.

Rear-engined 911: engine's center of mass is concentrated within the overhang, outside the wheelbase. Excessive weight that is concentrated outside of the wheelbase can interfere with accurate negotiation of corners at high speed. The rear-engined Porsche 911, with its engine far in the rear, was notorious for dangerous oversteer in its early days, and cars with engines far in the front often suffered from the opposite problem of understeer, for which many old American cars with heavy V8 engines were infamous. Front-engined Ferraris, such as the Ferrari 612 Scaglietti place their engines within the wheelbase, so as to avoid the problem of understeer.

Each end of a tree is a green, leafy tuft. An integral tree tuft is up to 50 kilometers from the tree's center of mass. Thus, a tuft is either orbiting too slowly (the "in" tuft) or too quickly (the "out" tuft) compared to the atmosphere, which is in orbit at all points. The ends of the tree are therefore subject to a constant gale-force wind that causes the ends to curve into the shape of an integral symbol ∫ and pushes water and food onto the tufts, or (less forcefully) onto the trunk, where the gravity-like tidal forces pull the material out towards the tufts.

A binary system is a system of two astronomical bodies which are close enough that their gravitational attraction causes them to orbit each other around a barycenter (also see animated examples). More restrictive definitions require that this common center of mass is not located within the interior of either object, in order to exclude the typical planet–satellite systems and planetary systems. The most common binary systems are binary stars and binary asteroid, but brown dwarfs, planets, neutron stars, black holes and galaxies can also form binaries. A multiple system is like a binary system but consists of three or more objects such as for trinary stars and trinary asteroids.

Since the late 1980s it has been apparent that not only the Local Group, but all matter out to a distance of at least 50 Mpc is experiencing a bulk flow on the order of 600 km/s in the direction of the Norma Cluster (Abell 3627). Lynden-Bell et al. (1988) dubbed the cause of this the "Great Attractor". The Great Attractor is now understood to be the center of mass of an even larger structure of galaxy clusters, dubbed "Laniakea", which includes the Virgo Supercluster (including the Local Group) as well as the Hydra- Centaurus Supercluster, the Pavo-Indus Supercluster, and the Fornax Group.

Schematic diagram of scuba manifold systems Longer and deeper dives require a greater amount of breathing gas, in turn requiring higher filling pressure, a larger cylinder or multiple cylinders. A large diameter cylinder tends to move the diver's center of mass further from the centreline, making them unbalanced in the water, and a higher pressure cylinder has a similar effect, also reducing the buoyancy of the diver, due to the thicker metal required for strength. Cylinder length is also limited by ergonomic considerations in proportion to the height of the diver. A single cylinder also presents a critical single point of failure for the breathing gas supply.

One of the earliest photos of the kink instability in action - the 3 by 25 cm pyrex tube at Aldermaston. A kink instability (also kink oscillation or kink mode), is a current-driven plasma instability characterized by transverse displacements of a plasma column's cross-section from its center of mass without any change in the characteristics of the plasma. It typically develops in a thin plasma column carrying a strong axial current which exceeds the Kruskal–Shafranov limit and is sometimes known as the Kruskal–Shafranov (kink) instability. The kink instability was first widely explored in fusion power machines with Z-pinch configurations in the 1950s.

Balancing a bicycle by keeping the wheels under the center of mass When discussing bike balance, it is necessary to distinguish carefully between "stability", "self-stability", and "controllability". Recent research suggests that "rider-controlled stability of bicycles is indeed related to their self-stability." A bike remains upright when it is steered so that the ground reaction forces exactly balance all the other internal and external forces it experiences, such as gravitational if leaning, inertial or centrifugal if in a turn, gyroscopic if being steered, and aerodynamic if in a crosswind. Steering may be supplied by a rider or, under certain circumstances, by the bike itself.

This self-stability is generated by a combination of several effects that depend on the geometry, mass distribution, and forward speed of the bike. Tires, suspension, steering damping, and frame flex can also influence it, especially in motorcycles. Even when staying relatively motionless, a rider can balance a bike by the same principle. While performing a track stand, the rider can keep the line between the two contact patches under the combined center of mass by steering the front wheel to one side or the other and then moving forward and backward slightly to move the front contact patch from side to side as necessary.

A top- heavy bike can require more effort to keep upright, when stopped in traffic for example, than a bike which is just as tall but with a lower center of mass. This is an example of a vertical second-class lever. A small force at the end of the lever, the seat or handlebars at the top of the bike, more easily moves a large mass if the mass is closer to the fulcrum, where the tires touch the ground. This is why touring cyclists are advised to carry loads low on a bike, and panniers hang down on either side of front and rear racks.

The load borne by the two wheels varies not only with center of mass location, which in turn varies with the amount and location of passengers and luggage, but also with acceleration and deceleration. This phenomenon is known as load transfer or weight transfer, depending on the author, and provides challenges and opportunities to both riders and designers. For example, motorcycle racers can use it to increase the friction available to the front tire when cornering, and attempts to reduce front suspension compression during heavy braking has spawned several motorcycle fork designs. The net aerodynamic drag forces may be considered to act at a single point, called the center of pressure.

The aft end is formed in a rounded shape (blunt body), as this forms a shock wave that doesn't touch the capsule, and the heat is deflected away rather than melting the vehicle. The Apollo Command Module reentered with the center of mass offset from the center line; this caused the capsule to assume an angled attitude through the air, providing a sideways lift to be used for directional control. Rotational thrusters were used to steer the capsule under either automatic or manual control by changing the lift vector. At lower altitudes and speeds parachutes are used to slow the capsule down by making more drag.

MAXI J1659-152 is a rapidly rotating black-hole/star system, discovered by NASA's Swift space telescope on September 25, 2010. On March 19, 2013, ESA's XMM-Newton space telescope has helped to identify a star and a black hole that orbit each other at the rate of once every 2.4 hours. The black hole and the star orbit their common center of mass. Because the star is the lighter object, it lies farther from this point and has to "travel around its larger orbit at a breakneck speed of two million kilometers per hour", 500 to 600 km/s, or about 20 times Earth's orbital velocity.

Unlike the ARX-01, the ARX-02 is a bespoke LMP designed entirely for Acura by Wirth Research. The original 3.4L V8 was expanded to 4 liters for more durability and drivability with the larger power developed with P1 rules. Wirth Research developed a chassis to generate as much mechanical grip to overcome the power deficit to Diesel centric rules created by the ACO by exploiting the engine's low mass (low compared to larger Diesel engines). Rear tires are now fitted onto the front of the car, increasing the contact patch by 7%, indicating that the vehicle center of mass was more forward placed than its contemporaries.

A similar design was already tested on a smaller laser reflector carried on board of the METEOR-3M spacecraft launched on December 10, 2001. The purpose of the mission was to validate the spherical glass retroreflector satellite concept and obtain SLR (Satellite Laser Ranging) data for solution of scientific problems in geophysics, geodynamics, and relativity. The BLITS allows millimeter and submillimeter accuracy SLR measurements, as its "target error" (uncertainty of reflection center relative to its center of mass) is less than 0.1 mm. An additional advantage is that the Earth's magnetic field does not affect the satellite orbit and spin parameters, unlike retroreflectors incorporated into active satellites.

This frame is also called the center-of-mass frame, or center-of- momentum frame. The center-of-momentum frame is notable for being the reference frame in which the total energy (total relativistic energy) of a particle or compound object, is also the invariant mass (times the scale- factor speed of light squared). It is also the reference frame in which the object or system has minimum total energy. In both special relativity and general relativity it is essential to specify the rest frame of any time measurements, as the time that an event occurred is dependent on the rest frame of the observer.

Given the orbital eccentricity of this object, its orbital period is not a fixed value, because it is frequently perturbed by the gravity of the planets. Near perihelion, using an August 2011 epoch, Kazuo Kinoshita shows C/2010 X1 to have a heliocentric orbital period of 600,000 years, though more perturbations will occur. For objects at such high eccentricity, the Sun's barycentric coordinates are more stable than heliocentric coordinates. The orbit of a long-period comet is properly obtained when the osculating orbit is computed at an epoch after leaving the planetary region and is calculated with respect to the center of mass of the Solar System.

Active bearings have several advantages: they do not suffer from wear, have low friction, and can often accommodate irregularities in the mass distribution automatically, allowing rotors to spin around their center of mass with very low vibration. Passive magnetic bearings use permanent magnets and, therefore, do not require any input power but are difficult to design due to the limitations described by Earnshaw's theorem. Techniques using diamagnetic materials are relatively undeveloped and strongly depend on material characteristics. As a result, most magnetic bearings are active magnetic bearings, using electromagnets which require continuous power input and an active control system to keep the load stable.

A molecule in the gas phase is free to rotate relative to a set of mutually orthogonal axes of fixed orientation in space, centered on the center of mass of the molecule. Free rotation is not possible for molecules in liquid or solid phases due to the presence of intermolecular forces. Rotation about each unique axis is associated with a set of quantized energy levels dependent on the moment of inertia about that axis and a quantum number. Thus, for linear molecules the energy levels are described by a single moment of inertia and a single quantum number, J, which defines the magnitude of the rotational angular momentum.

C/1992 J1 (Spacewatch) is a comet that was discovered 1 May 1992 by David Rabinowitz of the Spacewatch Project. This was the first comet to be discovered using an automated system. Using a generic heliocentric (two-body) solution calculated near the time of perihelion (closest approach to the Sun), it is estimated to have an aphelion (Q) (furthest distance from the Sun) of 154,202 AU (more than 2 Light-years). But the orbit of a long-period comet is properly obtained when the osculating orbit is computed at an epoch after leaving the planetary region and is calculated with respect to the center of mass of the solar system.

However, in the western roll the jumper's side or back faces the bar; in the straddle the jumper crosses the bar face down, with legs straddling it. With this clearance position, the straddle has a mechanical advantage over the western roll, since it is possible to clear a bar that is higher relative to the jumper's center of mass. In simple terms, the western roll jumper has to raise the width of the body above the bar; the straddle jumper has only to get the thickness of the body above it. There are two variants of the straddle: the parallel straddle and a more diving version.

It is instrumental for keeping time, in that UTC is essentially the atomic time synchronized to Earth's rotation by means of exact astronomical observations. Astrometry is an important step in the cosmic distance ladder because it establishes parallax distance estimates for stars in the Milky Way. Astrometry has also been used to support claims of extrasolar planet detection by measuring the displacement the proposed planets cause in their parent star's apparent position on the sky, due to their mutual orbit around the center of mass of the system. Astrometry is more accurate in space missions that are not affected by the distorting effects of the Earth's atmosphere.

Richard Douglas Fosbury (born March 6, 1947) is an American retired high jumper, who is considered one of the most influential athletes in the history of track and field. Besides winning a gold medal at the 1968 Olympics, he revolutionized the high jump event with a "back-first" technique, now known as the Fosbury Flop, adopted by almost all high jumpers today. His method was to sprint diagonally towards the bar, then curve and leap backwards over the bar, which gave him a much lower center of mass in flight than traditional techniques. He continues to be involved in athletics and serves on the executive board of the World Olympians Association.

Vectorial Mechanics has 18 chapters grouped into 3 parts. Part I is on vector algebra including chapters on a definition of a vector, products of vectors, elementary tensor analysis, and integral theorems. Part II is on systems of line vectors including chapters on line co-ordinates, systems of line vectors, statics of rigid bodies, the displacement of a rigid body, and the work of a system of line vectors. Part III is on dynamics including kinematics, particle dynamics, types of particle motion, dynamics of systems of particles, rigid bodies in motion, dynamics of rigid bodies, motion of a rigid body about its center of mass, gyrostatic problems, and impulsive motion.

The same is true for massless particles in such system, which add invariant mass and also rest mass to systems, according to their energy. For an isolated massive system, the center of mass of the system moves in a straight line with a steady sub-luminal velocity (with a velocity depending on the reference frame used to view it). Thus, an observer can always be placed to move along with it. In this frame, which is the center-of-momentum frame, the total momentum is zero, and the system as a whole may be thought of as being "at rest" if it is a bound system (like a bottle of gas).

In this frame, which exists under these assumptions, the invariant mass of the system is equal to the total system energy (in the zero-momentum frame) divided by . This total energy in the center of momentum frame, is the minimum energy which the system may be observed to have, when seen by various observers from various inertial frames. Note that for reasons above, such a rest frame does not exist for single photons, or rays of light moving in one direction. When two or more photons move in different directions, however, a center of mass frame (or "rest frame" if the system is bound) exists.

When used in cars, advantages of flat engines are a low center of mass (which improves the handling of the car), short length, low vibration and suitability for air cooling (due to the well exposed, large surface area, cylinder heads and short length). However the larger width of flat engines (compared with the more common inline and V layouts) is a drawback, particularly when the engine is located between the steered wheels. Flat engines were used by various automobile manufacturers— mostly with a boxer- four design— up until the late 1990s. Since then, only Porsche and Subaru have remained as significant manufacturers of flat engines.

Compared with an equivalent inline engine (the most common configuration for engines with less than six cylinders), a V engine has a shorter length but is wider. This effect increases with the number of cylinders in the engine; the length different between a V-twin and straight-twin engines might be insignificant, however V8 engines have a significantly smaller length than straight-eight engines. Compared with the less common flat engine, a V engine is narrower, taller and has a higher center of mass. V-angle illustrated by the yellow lines The "V-angle" (or "included angle") between the cylinder banks varies significantly between engines.

This could be due to a faulty measurement device (e.g. a meter stick), or, more likely, a systematic error in the use of that device in measuring L. This could occur if the students forgot to measure to the center of mass of the bob, and instead consistently measured to the point where the string attached to it. Thus, this error is not random; it occurs each and every time the length is measured. Next, the period of oscillation T could suffer from a systematic error if, for example, the students consistently miscounted the back-and-forth motions of the pendulum to obtain an integer number of cycles.

Directional stability is frequently called "weather vaning" because a directionally stable vehicle free to rotate about its center of mass is similar to a weather vane rotating about its (vertical) pivot. With the exception of spacecraft, vehicles generally have a recognisable front and rear and are designed so that the front points more or less in the direction of motion. Without this stability, they may tumble end over end, spin or orient themselves at a high angle of attack, even broadside on to the direction of motion. At high angles of attack, drag forces may become excessive, the vehicle may be impossible to control, or may even experience structural failure.

Semirigid rotor system The semirigid rotor can also be referred to as a teetering or seesaw rotor. This system is normally composed of two blades that meet just under a common flapping or teetering hinge at the rotor shaft. This allows the blades to flap together in opposite motions like a seesaw. This underslinging of the blades below the teetering hinge, combined with an adequate dihedral or coning angle on the blades, minimizes variations in the radius of each blade's center of mass from the axis of rotation as the rotor turns, which in turn reduces the stress on the blades from lead and lag forces caused by the Coriolis effect.

This is prominent on many types of racing cars, but is also used on most passenger cars to some degree, if only to counteract the tendency for the car to otherwise produce positive lift. In addition to providing increased adhesion, car aerodynamics are frequently designed to compensate for the inherent increase in oversteer as cornering speed increases. When a car corners, it must rotate about its vertical axis as well as translate its center of mass in an arc. However, in a tight-radius (lower speed) corner the angular velocity of the car is high, while in a longer-radius (higher speed) corner the angular velocity is much lower.

Block on a ramp and corresponding free body diagram of the block showing the surface force from the ramp onto the bottom of the block and separated into two components, a normal force N and a frictional shear force f, along with the body force of gravity mg acting at the center of mass. Surface force denoted fs is the force that acts across an internal or external surface element in a material body. Surface force can be decomposed into two perpendicular components: normal forces and shear forces. A normal force acts normally over an area and a shear force acts tangentially over an area.

Beyond the restrictions set forth by launch service providers, various technical challenges further reduce the usefulness of CubeSat propulsion. Gimbaled thrust cannot be used in small engines due to the complexity of gimbaling mechanisms, thrust vectoring must instead be achieved by thrusting asymmetrically in multiple-nozzle propulsion systems or by changing the center of mass relative to the CubeSat's geometry with actuated components. Small motors may also not have room for throttling methods that allow smaller than fully on thrust, which is important for precision maneuvers such as rendezvous. CubeSats which require longer life also benefit from propulsion systems, when used for orbit keeping a propulsion system can slow orbital decay.

A 3-simplex, with barycentric subdivisions of 1-faces (edges) 2-faces (triangles) and 3-faces (body). In geometry, a barycentric coordinate system is a coordinate system in which the location of a point is specified by reference to a simplex (a triangle for points in a plane, a tetrahedron for points in three-dimensional space, etc.). The barycentric coordinates of a point can be interpreted as masses placed at the vertices of the simplex, such that the point is the center of mass (or barycenter) of these masses. These masses can be zero or negative; they are all positive if and only if the point is inside the simplex.

A molecular vibration is a periodic motion of the atoms of a molecule relative to each other, such that the center of mass of the molecule remains unchanged. The typical vibrational frequencies, range from less than 1013 Hz to approximately 1014 Hz, corresponding to wavenumbers of approximately 300 to 3000 cm−1. In general, a non-linear molecule with N atoms has 3N – 6 normal modes of vibration, but a linear molecule has 3N – 5 modes, because rotation about the molecular axis cannot be observed. A diatomic molecule has one normal mode of vibration, since it can only stretch or compress the single bond.

In 1961, three years before a US astronaut walked in space, USAF Officer Whitsett imagined how astronauts could "fly" in space without tethers while working at the Air Force Institute of Technology (AFIT) at Wright-Patterson Air Force Base, Ohio. In 1962, he studied the human body's response to weightlessness. He developed the mathematical model for human mass distribution, center of mass, moments of inertia, and body movement. Whitsett used a Reduced-gravity aircraft to validate his model, but the test were inconclusive. He started work at NASA in 1966 while on assignment from the USAF as the experiment coordinator for the manned spaceflight program.

The "take-off" begins when the forelegs leave the ground and is completed when the hindlegs leave the ground. Once the horse leaves the ground, he is unable to influence the trajectory that his center of mass follows through the air, which makes take- off the most critical phase of the jumping process. Most of the energy required to clear an obstacle is produced by the hind legs. The longer the hindlegs are in contact with the ground, the greater their capacity for producing power; the further forward the hindlegs are placed under the body, closer to the obstacle, the longer this stance phase.

When the top end of the Slinky is dropped, the information of the tension change must propagate to the bottom end before both sides begin to fall; the top of an extended Slinky will drop while the bottom initially remains in its original position, compressing the spring. This creates a suspension time of ~0.3 s for an original Slinky, but has potential to create a much larger suspension time. A suspended Slinky's center of mass is accelerating downward at 16 feet per second per second (i.e., g); when released - the lower portion moves up toward the top portion with an equivalent, constant upward acceleration as the tension is relieved.

In the case of an individual standing quietly upright, the limit of stability is defined as the amount of postural sway at which balance is lost and corrective action is required. PDF Body sway can occur in all planes of motion, which make it an increasingly difficult ability to rehabilitate. There is strong evidence in research showing that deficits in postural balance is related to the control of medial-lateral stability and an increased risk of falling. To remain balanced, a person standing must be able to keep the vertical projection of their center of mass within their base of support, resulting in little medial-lateral or anterior-posterior sway.

This star system has an apparent visual magnitude of +3.0, making it one of the brighter stars in the constellation and hence readily visible to the naked eye. Parallax measurements from the Hipparcos mission yield a distance estimate of around from the Sun. This is a single-lined spectroscopic binary system, which means that the pair have not been individually resolved with a telescope, but the gravitational perturbations of an unseen astrometric companion can be discerned by shifts in the spectrum of the primary caused by the Doppler effect. The pair orbit around their common center of mass once every 675 days with an eccentricity of 0.57.

Tritium is an important fuel for controlled nuclear fusion in both magnetic confinement and inertial confinement fusion reactor designs. The experimental fusion reactor ITER and the National Ignition Facility (NIF) will use deuterium-tritium fuel. The deuterium-tritium reaction is favorable since it has the largest fusion cross section (about 5.0 barns) and it reaches this maximum cross section at the lowest energy (about 65 keV center-of-mass) of any potential fusion fuel. The Tritium Systems Test Assembly (TSTA) was a facility at the Los Alamos National Laboratory dedicated to the development and demonstration of technologies required for fusion-relevant deuterium- tritium processing.

The ship reaches periapsis where tidal forces nearly pull Shaeffer apart anyway, but he manages to hold himself in the access space at the ship's center of mass and survives. After returning to We Made It, Shaeffer is hospitalized (he has received a sunburn by starlight blue-shifted into the ultraviolet) for observation at the Puppeteer's insistence. While explaining tidal forces to the Puppeteer, Schaeffer realizes the alien had no knowledge of tides, something that would be elementary for a sentient species living on a world with a moon. The Puppeteers are extremely cautious when dealing with other races, and keep all details about their homeworld secret.

First evidence of parton energy loss has been observed at the Relativistic Heavy Ion Collider (RHIC) from the suppression of high-pt particles studying the nuclear modification factor and the suppression of back-to-back correlations. In ultra-relativistic heavy-ion collisions at center-of-mass energy of 2.76 and 5.02 TeV at the Large Hadron Collider (LHC), interactions between the high- momentum parton and the hot, dense medium produced in the collisions, are expected to lead to jet quenching. Indeed, in November 2010 CERN announced the first direct observation of jet quenching, based on experiments with heavy-ion collisions, which involved ATLAS, CMS and ALICE.

A 100-body simulation with the Barnes–Hut tree visually as blue boxes. The Barnes–Hut simulation (named after Josh Barnes and Piet Hut) is an approximation algorithm for performing an n-body simulation. It is notable for having order O(n log n) compared to a direct-sum algorithm which would be O(n2). The simulation volume is usually divided up into cubic cells via an octree (in a three-dimensional space), so that only particles from nearby cells need to be treated individually, and particles in distant cells can be treated as a single large particle centered at the cell's center of mass (or as a low-order multipole expansion).

The rocker-bogie design has no springs or stub axles for each wheel, allowing the rover to climb over obstacles (such as rocks) that are up to twice the wheel's diameter in size while keeping all six wheels on the ground. As with any suspension system, the tilt stability is limited by the height of the center of gravity. Systems using springs tend to tip more easily as the loaded side yields. Based on the center of mass, the Curiosity rover of the Mars Science Laboratory mission can withstand a tilt of at least 45 degrees in any direction without overturning, but automatic sensors limit the rover from exceeding 30-degree tilts.

In principle, electromagnetic radiation interacts with the surface of an asteroid in three significant ways: radiation from the Sun is (1) absorbed and (2) diffusively reflected by the surface of the body and the body's internal energy is (3) emitted as thermal radiation. Since photons possess momentum, each of these interactions leads to changes in the angular momentum of the body relative to its center of mass. If considered for only a short period of time, these changes are very small, but over longer periods of time, these changes may integrate to significant changes in the angular momentum of the body. For bodies in a heliocentric orbit, the relevant long period of time is the orbital period (i.e.

When operated as an accelerator for fixed-target experiments, the SPS can accelerate a beam to 450 GeV, before the beam is extracted within seconds (or a small fraction of a second when used to accelerate a bunches for injection into LHC). However, when operated as a collider, the beam has to be stored in the beam line for hours and the dipole magnets of the accelerator must keep a constant magnetic field for a longer time. To prevent overheating the magnets, the SpS would only accelerate the beams to a center-of-mass energy of 315 GeV. This limit could however be overcome by ramping the magnets between 100 GeV and the machines maximum capacity of 450 GeV.

This argument can be easily made rigorous by exhaustion by using little rectangles instead of infinitesimal lines, and this is what Archimedes does in On the Equilibrium of Planes. So the center of mass of a triangle must be at the intersection point of the medians. For the triangle in question, one median is the line y = x/2, while a second median is the line y = 1 − x. Solving these equations, we see that the intersection of these two medians is above the point x = 2/3, so that the total effect of the triangle on the lever is as if the total mass of the triangle were pushing down on (or hanging from) this point.

Traditional tail rotor of an Aérospatiale Puma Closeup view of the tail of a Robinson R44 The tail rotor is a smaller rotor mounted vertically or near- vertically at the tail of a traditional single-rotor helicopter, where it rotates to generate a horizontal thrust in the same direction as the main rotor's rotation. The tail rotor's position and distance from the helicopter's center of mass allow it to develop enough thrust leverage to counter the reactional torque exerted on the fuselage by the spinning of the main rotor. Without the tail rotor or other anti-torque mechansims (e.g. NOTAR), the helicopter would be constantly spinning in the opposite direction of the main rotor when flying.

This will naturally result in a push that starts on the center edge or on a slight outside edge and "rolls over" onto the inside edge as the foot moves away from the skater's center of mass. The double-push eliminates the "glide" phase from the above cycle, replacing it with a medially-directed "underpush" on the outside-edge. The recovery skate is placed on an outside edge and pushed underneath the body (right leg pushes leftward, and vice versa) while maintaining that outside edge, before being steered or pulled back across the centerline for the regular inside-edge push that follows. By its nature the double-push is less stable than classic technique, making it difficult to learn.

The objective of the UA4 experiment was to measure the antiproton-proton cross-section, in order to show that cross-sections rising with energy are true a characteristic of strong interaction. One had previously measured proton-antiproton cross-sections at the Intersecting Storage Rings, but as the Proton-Antiproton Collider — a modification of the Super Proton Synchrotron — began operating, the measurements could be done in a new energy range: up to 540 GeV center-of-mass energy. Elastic events were detected by high resolution wire chambers and scintillation-counter hodoscopes. A system of drift chamber telescopes and counter telescopes were placed on the left and the right side of the crossing region to detect inelastic events.

When early in the 1950s the plans for a European laboratory of particle physics began to take shape, two different accelerator projects emerged. One machine was to be of standard type, easy and relatively fast and cheap to build: the Synchrocyclotron, achieving collisions at a center-of-mass energy of 600 MeV. The second device was a much more ambitious undertaking: an accelerator bigger than any other then existing, a synchrotron that could accelerate protons up to an energy of 10 GeV — the PS. By May 1952 a design group was set up with Odd Dahl in charge. Other members of the group were among others Rolf Widerøe, Frank Kenneth Goward and John Adams.

The Gemini spacecraft was also equipped with a hypergolic Orbit Attitude and Maneuvering System, which made it the first crewed spacecraft with translation as well as rotation capability. In-orbit attitude control was achieved by firing pairs of eight thrusters located around the circumference of its adapter module at the extreme aft end. Lateral translation control was provided by four thrusters around the circumference at the forward end of the adaptor module (close to the spacecraft's center of mass). Two forward-pointing thrusters at the same location, provided aft translation, and two thrusters located in the aft end of the adapter module provided forward thrust, which could be used to change the craft's orbit.

Leonardo da Vinci researched the wing design of birds and designed a man-powered aircraft in his Codex on the Flight of Birds (1502), noting for the first time the distinction between the center of mass and the center of pressure of flying birds. In 1799, George Cayley set forth the concept of the modern airplane as a fixed-wing flying machine with separate systems for lift, propulsion, and control. Cayley was building and flying models of fixed-wing aircraft as early as 1803, and he built a successful passenger-carrying glider in 1853. In 1856, Frenchman Jean-Marie Le Bris made the first powered flight, by having his glider "L'Albatros artificiel" pulled by a horse on a beach.

The original GL1000 (designated K0) had an electric starter backed up by a kick start lever stored inside a dummy fuel tank, which also housed the radiator expansion tank, electrical components, as well as the air filter supplying four Keihin 32 mm CV carburetors. The real fuel tank was under the seat, in order to keep the center of mass as low as possible. The bike had a dry weight of . 13,000 Gold Wings were sold in the United States in 1975. There were no significant changes in the standard Gold Wing for 1976 (the K1 model). To mark the United States Bicentennial year Honda announced the GL1000 LTD with distinctive insignia and color scheme (e.g.

Its neck was flexible enough to allow it to keep sight of predators, as it could reach the sides of its body with its snout and look over the back. In addition, the posterior position of the center of mass may not have been advantageous for rapid locomotion, but meant that the animal could quickly rotate around the hips by pushing sideways with the arms, keeping the tail pointed at the attacker. Kentrosaurus was nevertheless not invulnerable. A quick predator could have made it to the tail base (where the impact speed would be much lower) when the tail passed and the neck and upper-part of the body would have been unprotected by the tail swings.

Once a round is fired and another is chambered, the empty shell falls downwards to the ground, pushed by its own weight. The design of the RMb-93 "Rys-K" carries several advantages: the ejection system makes the gun fully ambidextrous, and the magazine located over the barrel gives the shotgun a low center of mass and reduces upward recoil. The main drawback of the overall design stands in the fact that the weapon has a pistol grip with upfolding metal stock, which when folded finds itself right up the feeding tube. The RMb-93 thus can not be reloaded without extending or removing the stock, a disadvantage if it is being used tactically with a folded stock.

Currently, there are 3 main hypotheses suggesting how humans maintain postural stability while standing: # Stiffness of ankle joint: The stiffness model was first introduced by Winter et al., in 1998, and states that simple stiffness of ankle muscles account for the control of balance during quiet standing. The stiffness of the ankle muscle was determined experimentally by summing up the moments (or torque) left and right about the ankle and dividing it by the sway angle (angle at which the center of mass is displaced from the center of pressure). It was found in both analytical and experimental data (using human subjects) that there was a linear relationship between moments about the ankle muscle and sway angle.

Soldiers are instructed to fire at any target within this range by simply placing the sights on the center of mass (the belt buckle) of the enemy target. Any errors in range estimation are tactically irrelevant, as a well-aimed shot will hit the torso of the enemy soldier. An AKS-74U with accessories tuned by Zenitco The AKS-74U is significantly more maneuverable in tight quarters than the AKS-74; however, the significant decline in muzzle velocity to resulted in a reduction in effective range to (the effective hitting distance for a "running"-type silhouette target was reduced from to ). The AKS-74U cannot mount a bayonet or standard under-barrel grenade launcher.

But there are two essential differences between Archimedes' method and 19th- century methods: # Archimedes did not know about differentiation, so he could not calculate any integrals other than those that came from center-of-mass considerations, by symmetry. While he had a notion of linearity, to find the volume of a sphere he had to balance two figures at the same time; he never figured out how to change variables or integrate by parts. # When calculating approximating sums, he imposed the further constraint that the sums provide rigorous upper and lower bounds. This was required because the Greeks lacked algebraic methods that could establish that error terms in an approximation are small.

Clane has taken part of his army along with Czinczar and his army aboard the captured Riss ship, which he has renamed Solar Star, and has headed out on a one-year journey to a star sixty-five light-years from Sol. On arrival they discover two Earth-like planets revolving about their common center of mass as they go around their sun. The planets are occupied by humans, but Clane and his crew are shocked to discover that those people can teleport themselves and other things at will and that they have a peaceful trading relationship with the Riss. During the visit Clane and his crew engage and destroy a Riss battleship.

Tomb of the Diver, Paestum, Italy, a Greek fresco dated 470 BC At the moment of take-off, two critical aspects of the dive are determined, and cannot subsequently be altered during the execution. One is the trajectory of the dive, and the other is the magnitude of the angular momentum. The speed of rotation – and therefore the total amount of rotation – may be varied from moment to moment by changing the shape of the body, in accordance with the law of conservation of angular momentum. The center of mass of the diver follows a parabolic path in free- fall under the influence of gravity (ignoring the effects of air resistance, which are negligible at the speeds involved).

Under this proposal, Charon would have been classified as a planet, because the draft explicitly defined a planetary satellite as one in which the barycenter lies within the major body. In the final definition, Pluto was reclassified as a dwarf planet, but the formal definition of a planetary satellite was not decided upon. Charon is not in the list of dwarf planets currently recognized by the IAU. Had the draft proposal been accepted, even the Moon would be classified as a planet in billions of years when the tidal acceleration that is gradually moving the Moon away from Earth takes it far enough away that the center of mass of the system no longer lies within Earth.

The term binary was first used in this context by Sir William Herschel in 1802, when he wrote: By the modern definition, the term binary star is generally restricted to pairs of stars which revolve around a common center of mass. Binary stars which can be resolved with a telescope or interferometric methods are known as visual binaries. For most of the known visual binary stars one whole revolution has not been observed yet, they are observed to have travelled along a curved path or a partial arc. Binary system of two stars The more general term double star is used for pairs of stars which are seen to be close together in the sky.

In steady-state cornering, front-heavy cars tend to understeer and rear-heavy cars to oversteer (Understeer & Oversteer explained), all other things being equal. The mid-engine design seeks to achieve the ideal center of mass, though front- engine design has the advantage of permitting a more practical engine- passenger-baggage layout. All other parameters being equal, at the hands of an expert driver a neutrally balanced mid-engine car can corner faster, but a FR (front-engined, rear-wheel drive) layout car is easier to drive at the limit. The rearward weight bias preferred by sports and racing cars results from handling effects during the transition from straight-ahead to cornering.

Weight carried on a belt can be distributed to shift the weight forward or backward to change the position of the diver's center of mass. Systems that integrate the weights into the BCD, can provide improved comfort so long as the BCD does not have to be removed from the body of the diver, for example in an underwater emergency such as an entanglement. When a weight integrated BCD is removed, a diver wearing no weight-belt, and any type of wetsuit or dry suit, will be very buoyant. By inflating the BC at the surface, a conscious diver may be able to easily float face-up, depending on their equipment configuration choices.

Larger objects distort into an ovoid, and are slightly compressed, which is what happens to the Earth's oceans under the action of the Moon. The Earth and Moon rotate about their common center of mass or barycenter, and their gravitational attraction provides the centripetal force necessary to maintain this motion. To an observer on the Earth, very close to this barycenter, the situation is one of the Earth as body 1 acted upon by the gravity of the Moon as body 2. All parts of the Earth are subject to the Moon's gravitational forces, causing the water in the oceans to redistribute, forming bulges on the sides near the Moon and far from the Moon.

Taking the molecular center of mass as origin of coordinates, consider the change of all electrons' position from (xi, yi, zi) to (−xi, −yi, −zi). If the resulting wave function is unchanged, it is said to be gerade (German for even); if the wave function changes sign then it is said to be ungerade (odd). For a molecule with a center of inversion, all orbitals will be symmetric or antisymmetric. The resulting wavefunction for the whole multielectron system will be gerade if an even number of electrons are in ungerade orbitals, and ungerade if there are an odd number of electrons in ungerade orbitals, regardless of the number of electrons in gerade orbitals.

When the flying ice cube problem was first found, the Bussi–Donadio–Parrinello thermostat had not yet been developed, and it was desired to continue using the Berendsen thermostat due to the efficiency with which velocity rescaling thermostats relax systems to desired temperatures. Thus, suggestions were given to avoid the flying ice cube effect under the Berendsen thermostat, such as periodically removing the center-of-mass motions and using a longer temperature coupling time. However, more recently it has been recommended that the better practice is to discontinue use of the Berendsen thermostat entirely in favor of the Bussi–Donadio–Parrinello thermostat, as it has been shown that the latter thermostat does not exhibit the flying ice cube effect.

With the lowest center of mass among standard-sided cars at the time, the Hudson was praised for its great handling and roadworthiness so that stock car racers embraced these cars and "christened them with the 'Fabulous' prefix that followed this line through its days of track dominance." The combination of the car's light weight due to the advanced unibody construction that Hudson called 'step down' design, allowed Hudson drivers to win various stock car racing events from 1951 through 1954. Drivers "proved it could out-handle and out-accelerate much of its supposedly more powerful V-8 competition." The company used the "Fabulous Hudson Hornet, national stock car champion" description in its advertising.

Like Poincaré, Einstein concluded in 1906 that the inertia of electromagnetic energy is a necessary condition for the center-of-mass theorem to hold. On this occasion, Einstein referred to Poincaré's 1900 paper and wrote: In Einstein's more physical, as opposed to formal or mathematical, point of view, there was no need for fictitious masses. He could avoid the perpetuum mobile problem because, on the basis of the mass–energy equivalence, he could show that the transport of inertia that accompanies the emission and absorption of radiation solves the problem. Poincaré's rejection of the principle of action–reaction can be avoided through Einstein's , because mass conservation appears as a special case of the energy conservation law.

Front- wheel drive and a rear door give it a low loading height. With a 20 kg total increase in weight and a higher center of mass, wagon's ride is smoother than the sedan's but the handling is not as good in turns. The wagon was released with options that differ mainly by engine: basic VAZ-21110 With the "standard", "normal" and "luxury" (similar to a sedan car VAZ-21102) with a 1.5-liter 8-valve engine, "2111" and "top-end"VAZ-21113 to trim the" norm "and" luxury "with 16-valve engine," 2112 "and front ventilated disc brakes (like the sedan VAZ-21103). The "2111" and "2112" were equipped with fuel injection and catalytic converter.

The Tango is thinner than some motorcycles and may be small enough to legally ride side- by-side with other small vehicles in traffic lanes in some jurisdictions. Capable of seating two passengers in a tandem seating arrangement, it only takes up one-quarter of a standard parking space and is able to park sideways in many cases. One prototype vehicle has been produced by the company and was shipped to Prodrive in the United Kingdom in January 2005, where the design was refined for production models. Commuter Cars says the Tango's heavy battery pack and low ground-clearance combine to give it a center-of-mass from the ground, allowing for stable handling.

The fundamental requirement for static stability is that the aft surface must have greater authority (leverage) in restoring a disturbance than the forward surface has in exacerbating it. This leverage is a product of moment arm from the center of mass and surface area. Correctly balanced in this way, the partial derivative of pitching moment with respect to changes in angle of attack will be negative: a momentary pitch up to a larger angle of attack makes the resultant pitching moment tend to pitch the aircraft back down. (Here, pitch is used casually for the angle between the nose and the direction of the airflow; angle of attack.) This is the "stability derivative" d(M)/d(alpha), described below.

In a vehicle dynamics, the roll moment can be calculated as the product of three quantities: #the vehicle's sprung mass, the portion of its mass supported by the suspension, #whatever lateral acceleration that the vehicle is experiencing, usually centripetal acceleration from a turn, and #the vertical distance between the vehicle's roll axis and its center of mass. In two-axle vehicles, such as cars and some trucks, the roll axis may be found by connecting the roll center of each axle by a straight line. In single-track vehicles, such as bicycles and motorcycles, the roll axis may be found by connecting the contact patches of each tire by a straight line.

On 10 November, the 3rd Air Cavalry Brigade replaced the 1st Air Cavalry Brigade and the operations were shifted from west to east in a diversionary maneuver to entice the B3 Field Front to regroup its three regiments in assembly area to regain its early advantage with a second attack of the Pleime camp. It set the D-day for 16 November.Kinnard, p.73Vinh Loc, pp.79–80 On 11 November, the 66th Regiment was along the north bank of the Ia Drang (center of mass Vic YA 9104); the 32nd Regiment was also up north (YA 820070); and the 33rd Regiment was in the vicinity of the Anta Village (YA 940010).

MF layout In automotive design, a Front Mid-engine, Front-wheel-drive layout (sometimes called FMF or just MF) is one in which the front road wheels are driven by an internal-combustion engine placed just behind them, in front of the passenger compartment. In contrast to the Front-engine, front-wheel-drive layout (FF), the center of mass of the engine is behind the front axle. This layout is typically chosen for its better weight distribution (the heaviest component is near the center of the car, lowering its moment of inertia). Since the differences between the FF and MF layouts are minor, most people consider the MF layout to be the same as the FF layout.

A coxed quad scull, with a bow cox A bowloader is a crew shell (a type of boat used in rowing) in which the coxswain lies semi-supine in the bow, as opposed to the normal seated position at the stern. Bowloaders are often seen as coxed fours and also coxed pairs. Although a small number of bowloader eights exist, the larger boat's momentum means that a coxswain lying in the bows could be injured in a collision if the bow collapses. A bowloader is slightly faster than a stern-coxed boat, since the mass of the coxswain in the bow reduces porpoising, and the semi-supine position puts the coxswain's center of mass below the waterline, reducing roll.

Contact between the spacecraft and mission control could not be established for over 24 hours. The root cause of this incident has not been determined, but software and operational errors contributed to the severity of the anomaly. The original mission plan called for the four burns to be followed by an orbit insertion burn on January 10, 1999, but the abort of the first burn and loss of communication made this impossible. A new plan was put into effect in which NEAR flew by Eros on December 23, 1998 at 18:41:23 UT at a speed of 965 m/s and a distance of 3827 km from the center of mass of Eros.

Animals with elongated bodies and reduced or no legs have evolved differently from their limbed relatives. In the past, some have speculated that this evolution was due to a lower energetic cost associated with limbless locomotion. The biomechanical arguments used to support this rationale include that (1) there is no cost associatied with the vertical displacement of the center of mass typically found with limbed animals, (2) there is no cost associated with accelerating or decelerating limbs, and (3) there is a lower cost for supporting the body. This hypothesis has been studied further by examining the oxygen consumption rates in the snake during different modes of locomotion: lateral undulation, concertina, and sidewinding.

In physics (specifically, celestial mechanics), escape velocity is the minimum speed needed for a free, non-propelled object to escape from the gravitational influence of a massive body, that is, to achieve an infinite distance from it. Escape velocity is a function of the mass of the body and distance to the center of mass of the body. A rocket, continuously accelerated by its exhaust, need not reach ballistic escape velocity at any distance since it is supplied with additional kinetic energy by the expulsion of its reaction mass. It can achieve escape at any speed, given a suitable mode of propulsion and sufficient propellant to provide the accelerating force on the object to escape.

If an object attains exactly escape velocity, but is not directed straight away from the planet, then it will follow a curved path or trajectory. Although this trajectory does not form a closed shape, it can be referred to as an orbit. Assuming that gravity is the only significant force in the system, this object's speed at any point in the trajectory will be equal to the escape velocity at that point due to the conservation of energy, its total energy must always be 0, which implies that it always has escape velocity; see the derivation above. The shape of the trajectory will be a parabola whose focus is located at the center of mass of the planet.

An important element in maximising vertical jump height is an immediately preceding crouching action which preloads the muscles. This crouching action is usually performed quickly and referred to as a counter-movement: the rapid bending of the legs and the movement of the arms to the person's sides constitute the counter-movement to the actual jumps range of movement. The counter-movement and the jump collectively are referred to as a counter-movement jump (CMJ). The counter-movement of the legs, a quick bend of the knees which lowers the center of mass prior to springing upwards, has been shown to improve jump height by 12% compared to jumping without the counter-movement.

Because the average crew member would spend much time in these ships (around 16 months of transit plus rotating shifts in Mars orbit), habitat design for the ships was an integral part of this mission. Von Braun was aware of the threat posed by extended exposure to weightlessness. He suggested either tethering passenger ships together to spin about a common center of mass or including self-rotating, dumbbell-shaped "gravity cells" to drift alongside the flotilla to provide each crew member with a few hours of artificial gravity each day. At the time of von Braun's proposal, little was known of the dangers of solar radiation beyond Earth and it was cosmic radiation that was thought to present the more formidable challenge.

A front precise and stable, with good traction and drive, low center of mass, and aerodynamic efficiency were the key words of the successes but especially the high power-to-weight ratio that put out the qualities of the pilot. It is no coincidence Jim Pauley (who also rans at Le Mans), Dave Michaels, and Tom O'Brien collected the best results in years when Bandinis (powered by Siata, Offenhauser, and Alfa Romeo) run in SCCA's FM (F Modified) category alongside Ferraris, Maseratis, and Porsches. Michaels in a 1625cc (99 ci) Bandini-Offy for a year and half held the Thompson track record in the under-two liter class. Speed and quality showed the under-750 category, in the hands of Dolph Vilardi (U.

It can be suspended stably in this inverted position by using a control system to monitor the angle of the pole and move the pivot point horizontally back under the center of mass when it starts to fall over, keeping it balanced. The inverted pendulum is a classic problem in dynamics and control theory and is used as a benchmark for testing control strategies. It is often implemented with the pivot point mounted on a cart that can move horizontally under control of an electronic servo system as shown in the photo; this is called a cart and pole apparatus.C.A. Hamilton Union College Senior Project 1966 Most applications limit the pendulum to 1 degree of freedom by affixing the pole to an axis of rotation.

The sphere-cone is a spherical section with a frustum or blunted cone attached. The sphere-cone's dynamic stability is typically better than that of a spherical section. The vehicle enters sphere-first. With a sufficiently small half-angle and properly placed center of mass, a sphere-cone can provide aerodynamic stability from Keplerian entry to surface impact. (The half-angle is the angle between the cone's axis of rotational symmetry and its outer surface, and thus half the angle made by the cone's surface edges.) Prototype of the Mk-2 Reentry Vehicle (RV), based on blunt body theory. The original American sphere-cone aeroshell was the Mk-2 RV (reentry vehicle), which was developed in 1955 by the General Electric Corp.

This means that if the original uncut parabola is hung by a hook from the point x = −1 (so that the whole mass of the parabola is attached to that point), it will balance the triangle sitting between x = 0 and x = 1\. The center of mass of a triangle can be easily found by the following method, also due to Archimedes. If a median line is drawn from any one of the vertices of a triangle to the opposite edge E, the triangle will balance on the median, considered as a fulcrum. The reason is that if the triangle is divided into infinitesimal line segments parallel to E, each segment has equal length on opposite sides of the median, so balance follows by symmetry.

This 72-degree angle allows for even firing from the pistons without the use of a split- journal crankshaft, thus improving engine efficiency as well as lowering the overall weight. Dry sump lubrication prevents engine oil starvation through high-speed corners and lowers the engine's center of mass. Air is fed directly from beneath the hood through a visible slit passing into a dual-stage variable intake manifold and then into ten individual throttle bodies before finally exiting from a dual-stage titanium muffler. LFA Deputy Chief Engineer Chiharu Tamura explains LFA engine The LFA's engineers selected a V10 engine over an equivalent displacement V8 engine for its ability to rev higher,, and over a V12 for its lower reciprocating mass, allowing for more rapid engine response.

Mobile suits performing AMBAC motions would presumably move similarly to present-day astronauts performing extra-vehicular activity: both typically having roughly similar body structure, their use of that mass to control their rotation would presumably be similar, even if calculated by different means. AMBAC is by its nature limited to re-orienting the unit about its center of mass, and is not a substitute for propulsion. It is often used in conjunction with the propulsion system to quickly turn the unit and shorten aiming speed as well as directing the main thrusters. The system is similar in principle to the momentum wheel system used in present-day satellites, though obviously more complex and allows the centre of mass move outside of the unit.

Experimentation and mathematical analysis have shown that a bike stays upright when it is steered to keep its center of mass over its wheels. This steering is usually supplied by a rider, or in certain circumstances, by the bike itself. Several factors, including geometry, mass distribution, and gyroscopic effect all contribute in varying degrees to this self-stability, but long-standing hypotheses and claims that any single effect, such as gyroscopic or trail, is solely responsible for the stabilizing force have been discredited. While remaining upright may be the primary goal of beginning riders, a bike must lean in order to maintain balance in a turn: the higher the speed or smaller the turn radius, the more lean is required.

While countersteering is usually initiated by applying torque directly to the handlebars, on lighter vehicles such as bicycles, it can also be accomplished by shifting the rider's weight. If the rider leans to the right relative to the bike, the bike leans to the left to conserve angular momentum, and the combined center of mass remains nearly in the same vertical plane. This leftward lean of the bike, called counter lean by some authors, will cause it to steer to the left and initiate a right-hand turn as if the rider had countersteered to the left by applying a torque directly to the handlebars. This technique may be complicated by additional factors such as headset friction and stiff control cables.

More formally, this follows from the properties of the vector product, and shows that rotational effect of the force depends only on the position of its line of application, and not on the particular choice of the point of application along that line. The torque vector is perpendicular to the plane defined by the force and the vector \scriptstyle \vec r , and in this example it is directed towards the observer; the angular acceleration vector has the same direction. The right hand rule relates this direction to the clockwise or counter-clockwise rotation in the plane of the drawing. The moment of inertia \scriptstyle I is calculated with respect to the axis through the center of mass that is parallel with the torque.

Postural instability in upright stance is common in end-stage PD and compromises the ability to maintain balance during everyday tasks such as walking, turning and standing up from sitting. An inability to adequately balance the body's center of mass over the base of support combined with inflexibility in body movements (due to increased rigidity) causes patients with advanced PD to fall. Whereas postural sway in normal stance usually increases in patients with balance disorders arising from stroke, head injury and cerebellar ataxia it is often reduced in patients with PD. The reason for this because in PD the problem appears to be a lack of flexibility in shifting postural responses. This inflexibility increases the tendency to fall in these patients.

A pentagonal rosette as described in Larry Niven's novel Ringworld. The term "Klemperer rosette" (often misspelled "Kemplerer rosette") is often used to mean a configuration of three or more equal masses, set at the points of an equilateral polygon and given an equal angular velocity about their center of mass. Klemperer does indeed mention this configuration at the start of his article, but only as an already known set of equilibrium systems before introducing the actual rosettes. In Larry Niven's novel Ringworld, the Puppeteers' "Fleet of Worlds" is arranged in such a configuration (5 planets spaced at the points of a pentagon), which Niven calls a "Kemplerer rosette"; this (possibly intentional) misspelling (and misuse) is one possible source of this confusion.

This contradiction is caused by the fact that Noether's theorem is usually formulated for closed systems. The periodic cell exchanges mass momentum, angular momentum, and energy with the neighboring cells. When applied to the microcanonical ensemble (constant particle number, volume, and energy, abbreviated NVE), using PBC rather than reflecting walls slightly alters the sampling of the simulation due to the conservation of total linear momentum and the position of the center of mass; this ensemble has been termed the "molecular dynamics ensemble" or the NVEPG ensemble. These additional conserved quantities introduce minor artifacts related to the statistical mechanical definition of temperature, the departure of the velocity distributions from a Boltzmann distribution, and violations of equipartition for systems containing particles with heterogeneous masses.

RMR layout; the engine is located in front of the rear axle. Rear Mid-engine transversely-mounted / Rear-wheel drive In automotive design, a RMR or Rear Mid-engine, Rear-wheel-drive layout (now simply known as MR or Mid-engine, Rear-wheel-drive layout) is one in which the rear wheels are driven by an engine placed just in front of them, behind the passenger compartment. In contrast to the rear-engined RR layout, the center of mass of the engine is in front of the rear axle. This layout is typically chosen for its low moment of inertia and relatively favorable weight distribution (the heaviest component is within the wheelbase, making the main component of its moment of inertia relatively low).

To combat this, higher-numbered iron clubheads are heavier than lower-numbered iron heads; there is generally a increase in mass between one clubhead and the next higher number. Due to the average golfer's desire to hit the ball farther, the loft on modern irons is much less than that on irons from even the late 20th century. For example, a modern 9-iron has comparable loft to a 7-iron from the 1990s. Manufacturers have been able to reduce loft without compromising usability, by moving weight into the sole of the clubhead, thereby lowering the center of gravity and enabling the ball to be launched on a higher trajectory for a given loft than a design with a higher center of mass.

High-racer aficionados also claim that they are more stable, and although it is easier to balance a bicycle with a higher center of mass, the wide variety of recumbent designs makes such generalizations unreliable. Another advantage of both wheels being the same size is that the bike requires only one size of inner tube. One common arrangement is an ISO 559 (26-inch) rear wheel and an ISO 406 or ISO 451 (20-inch) front wheel. The small front wheel and large rear wheel combination is used to keep the pedals and front wheel clear of each other, avoiding the problem on a short wheelbase recumbent called "heel strike" (where the rider's heels catch the wheel in tight turns).

The "point-blank range" battle zero setting "П" standing for постоянная (constant) the 5.45×39mm AK-74 rear tangent sight element corresponds to a zero, compared with the zero for 7.62×39mm AKs. For the AK-74 combined with the 7N6 or 7N10 service cartridges the 400 m battle zero setting point-blank range limits the apparent "bullet rise" within approximately under the line of sight. At the corresponding maximum point-blank range the bullet will have dropped to approximately relative to the line of sight. Soldiers are instructed to fire at any target within this range by simply placing the sights on the center of mass (the belt buckle, according to Russian and former Soviet doctrine) of the enemy target.

Any device that is attached to the end of the muzzle will also add mass, increasing its inertia and moving its center of mass forward; the former will reduce recoil and the latter will reduce muzzle rise. The AKM rifle's slant-cut muzzle brake Construction of a muzzle brake or compensator can be as simple as a diagonal cut at the muzzle end of the barrel to direct some of the escaping gas upward. On the AKM assault rifle, the brake also angles slightly to the right to counteract the sideways movement of the rifle under recoil. Another simple method is porting, where holes or slots are machined into the barrel near the muzzle to allow the gas to escape.

Flat engines offer several advantages for motorcycles including a low center of mass, low vibration, suitability for shaft drive, and even cooling of the cylinders (for air-cooled engines). The most common design of flat engines for motorcycles is the boxer-twin, beginning with the 1905 Fée manufactured by the Light Motors Company flat- twin, which was the first production motorcycle to use a flat engine. BMW Motorrad have a long history of boxer-twin motorcycles, beginning in 1923 with the BMW R32 Several motorcycles have been produced with flat-four engines, such as the 1938-1939 Zündapp K800 and the 1974-1987 Honda Gold Wing. In 1987, the Honda Gold Wing engine was upsized to a flat-six design.

The center of mass (barycenter) of the Pluto–Charon system lies outside either body. Because neither object truly orbits the other, and Charon has 12.2% the mass of Pluto, it has been argued that Charon should be considered to be part of a binary system with Pluto. The International Astronomical Union (IAU) states that Charon is considered to be just a satellite of Pluto, but the idea that Charon might be classified a dwarf planet in its own right may be considered at a later date. In a draft proposal for the 2006 redefinition of the term, the IAU proposed that a planet be defined as a body that orbits the Sun that is large enough for gravitational forces to render the object (nearly) spherical.

The jacket of the very-low-drag bullet on the right provides an aerodynamic windscreen enclosing a hollow void so the center of mass of the lead core remains within the full diameter portion of the bullet to minimize misalignment with the bore axis. Soft-point bullets are similar to jacketed hollow-point bullets, because both have a jacket open on the forward tip. The soft core is exposed forward of the jacket on soft-point bullets, while the jacket may extend forward of the core on hollow-point bullets emphasizing aerodynamic improvement rather than expansion. Bullets with a large amount of core exposed forward of the jacket might have a hollow point within that core; and some hollow-point bullets have no jackets.

Algol B orbits Algol A. This animation was assembled from 55 images of the CHARA interferometer in the near-infrared H-band, sorted according to orbital phase. Sometimes, the only evidence of a binary star comes from the Doppler effect on its emitted light. In these cases, the binary consists of a pair of stars where the spectral lines in the light emitted from each star shifts first towards the blue, then towards the red, as each moves first towards us, and then away from us, during its motion about their common center of mass, with the period of their common orbit. In these systems, the separation between the stars is usually very small, and the orbital velocity very high.

Parabolic (1) and hyperbolic (3) orbits are escape orbits, whereas elliptical and circular orbits (2) are captive. gravitational potential well of the central mass's field of potential energy shown in black and the height of the kinetic energy of the moving body shown in red extending above that, correlating to changes in speed as distance changes according to Kepler's laws. Isaac Newton demonstrated that Kepler's laws were derivable from his theory of gravitation and that, in general, the orbits of bodies subject to gravity were conic sections (this assumes that the force of gravity propagates instantaneously). Newton showed that, for a pair of bodies, the orbits' sizes are in inverse proportion to their masses, and that those bodies orbit their common center of mass.

The tidal force is a force that stretches a body towards and away from the center of mass of another body due to a gradient (difference in strength) in gravitational field from the other body; it is responsible for diverse phenomena, including tides, tidal locking, breaking apart of celestial bodies and formation of ring systems within the Roche limit, and in extreme cases, spaghettification of objects. It arises because the gravitational field exerted on one body by another is not constant across its parts: the nearest side is attracted more strongly than the farthest side. It is this difference that causes a body to get stretched. Thus, the tidal force is also known as the differential force, as well as a secondary effect of the gravitational field.

The maniraptor model loading is typical for ducks, though these have a relatively larger wingspan and a lower aspect ratio. The bat model has a loading typical for shore birds, though again their wingspan is (much) larger while their aspect ratio to the contrary is higher. A problem for the hypothesis that Yi was specialised for gliding flight, resides in the fact that because of it having a forelimb wing, instead of a gliding skin along its torso as with most gliders, its center of mass seems to be behind its control and main lift surfaces, causing flight instability. This problem might have been lessened by a short fleshy tail and long tail feathers, as known from its relative Epidexipteryx.

CLEO was a general purpose particle detector at the Cornell Electron Storage Ring (CESR), and the name of the collaboration of physicists who operated the detector. The name CLEO is not an acronym; it is short for Cleopatra and was chosen to go with CESR (pronounced Caesar).Berkelman (2004) p. 24 CESR was a particle accelerator designed to collide electrons and positrons at a center- of-mass energy of approximately 10 GeV. The energy of the accelerator was chosen before the first three bottom quark Upsilon resonances were discovered between 9.4 GeV and 10.4 GeV in 1977. The fourth Υ resonance, the Υ(4S), was slightly above the threshold for, and therefore ideal for the study of, B meson production.

SimCraft, a privately held company headquartered just outside Atlanta, Georgia, is the creator of a proprietary motion simulation technology and manufactures simulation equipment integrating this technology, including professional driver in the loop racing simulators. The motion simulator technology, in development since 1998, is designed to recreate the manner in which vehicles move in earth physics. The company offers a range of simulator products in the category of motion simulation that provide a tactile true motion experience for Motorsport Simulation (sometimes referred to as simracing) and flight simulation. The company's core innovation and technology is the simulation of vehicle (motorsport & aviation based) movement through proprietary physics based software interfaces and a patent pending hardware architecture based on Center of Mass principles of motion.

To see that the incenter of the medial triangle coincides with the intersection point of the cleavers, consider a homogeneous wireframe in the shape of triangle ABC consisting of three wires in the form of line segments having lengths a, b, c. The wire frame has the same center of mass as a system of three particles of masses a, b, c placed at the midpoints D, E, F of the sides BC, CA, AB. The centre of mass of the particles at E and F is the point P which divides the segment EF in the ratio c : b. The line DP is the internal bisector of ∠D. The centre of mass of the three particle system thus lies on the internal bisector of ∠D.

On December 15, 2015, the ATLAS and CMS collaborations at CERN presented results from the second operational run of the Large Hadron Collider (LHC) at the center of mass energy of 13 TeV, the highest ever achieved in proton-proton collisions. Among the results, the invariant mass distribution of pairs of high-energy photons produced in the collisions showed an excess of events compared to the Standard Model prediction at around 750 GeV/c2. The statistical significance of the deviation was reported to be 3.9 and 3.4 standard deviations (locally) respectively for each experiment. The excess could have been explained by the production of a new particle (the digamma) with a mass of about 750 GeV/c2 that decayed into two photons.

In space an object maintains its orbit because of the force of gravity acting upon it. Planets orbit stars, stars orbit galactic centers, galaxies orbit a center of mass in clusters, and clusters orbit in superclusters. The force of gravity exerted on one object by another is directly proportional to the product of those objects' masses and inversely proportional to the square of the distance between them. The earliest gravity (possibly in the form of quantum gravity, supergravity or a gravitational singularity), along with ordinary space and time, developed during the Planck epoch (up to 10−43 seconds after the birth of the Universe), possibly from a primeval state (such as a false vacuum, quantum vacuum or virtual particle), in a currently unknown manner.

Otherwise, if we want to calculate the attraction between massive bodies, we need to add all the point-point attraction forces vectorially and the net attraction might not be exact inverse square. However, if the separation between the massive bodies is much larger compared to their sizes, then to a good approximation, it is reasonable to treat the masses as a point mass located at the object's center of mass while calculating the gravitational force. As the law of gravitation, this law was suggested in 1645 by Ismael Bullialdus. But Bullialdus did not accept Kepler's second and third laws, nor did he appreciate Christiaan Huygens's solution for circular motion (motion in a straight line pulled aside by the central force).

Based on a field recording in the Rocky Mountains of Canada of the Oreamnos americanus climbing a 45-degree slope, researchers were able to measure the goat's whole body movement as it climbed. Researchers observed that when the goat propelled itself forward, it extended its back legs and the front legs were tucked close up to its chest during its first phase. During the second phase the goat raised its back legs near to its chest, while the front legs humerus stayed locked in a persistent location relative to the goat's chest, therefore allowing the elbow to be detained in close proximity to the whole body's center of balance. Extension of the elbow and carpal joints resulted in a vertical translation of the center of mass up the mountain slope.

At the Lagrange points the gravitational forces of the two large bodies cancel out in such a way that a small object placed in orbit there is in equilibrium relative to the center of mass of the large bodies. There are five such points, labeled L1 to L5, all in the orbital plane of the two large bodies. L1, L2, and L3 are on the line through the centers of the two large bodies, while L4 and L5 each act as the third vertex of an equilateral triangle formed with the centers of the two large bodies. L1, L2, L3 are unstable equilibria, whereas L4 and L5 are stable, which implies that objects can orbit around them in a rotating coordinate system tied to the two large bodies.

Several variants of the double pendulum may be considered; the two limbs may be of equal or unequal lengths and masses, they may be simple pendulums or compound pendulums (also called complex pendulums) and the motion may be in three dimensions or restricted to the vertical plane. In the following analysis, the limbs are taken to be identical compound pendulums of length and mass , and the motion is restricted to two dimensions. Double compound pendulum Motion of the double compound pendulum (from numerical integration of the equations of motion) Trajectories of a double pendulum In a compound pendulum, the mass is distributed along its length. If the mass is evenly distributed, then the center of mass of each limb is at its midpoint, and the limb has a moment of inertia of about that point.

The hypothesis that Spinosaurus had a typical quadrupedal gait since fell out of favor, however it was still believed that spinosaurids may have crouched in a quadrupedal posture, due to biological and physiological constraints. Reconstructed foot, note straight claws and large hallux The possibility of a quadrupedal Spinosaurus was revived by a 2014 paper by Ibrahim and colleagues that described new material of the animal. The paper found that the hind limbs of Spinosaurus were much shorter than previously believed, and that its center of mass was located in the midpoint of the trunk region, as opposed to near the hip as in typical bipedal theropods. It was therefore proposed that Spinosaurus was poorly adapted for bipedal terrestrial locomotion, and must have been an obligate quadruped on land.

When the pilot moves the cyclic forward to pitch the nose down and accelerate forward, the helicopter responds by decreasing collective pitch on the front rotor and increases collective pitch on the rear rotor proportionally, pivoting the two ends around their common center of mass. Changes in yaw are made with differential cyclic pitch, the front rotor altering cyclic pitch in the direction desired and the opposite pitch applied to the rear, once again pivoting the craft around its center. Conversely, the synchropter and transverse-mounted rotor counter rotating rotorcraft have two large horizontal rotor assemblies mounted side by side, (like a Bell/Boeing V-22 tilt rotor) helicopters use differential collective pitch to affect the roll of the aircraft. Like tandem rotors, differential cyclic pitch is used to control movement about the yaw axis.

Carryover cooking (sometimes referred to as resting) is when foods are halted from actively cooking and allowed to equilibrate under their own retained heat. Because foods such as meats are typically measured for cooking temperature near the center of mass, stopping cooking at a given central temperature means that the outer layers of the food will be at higher temperature than that measured. Heat therefore will continue to migrate inwards from the surface, and the food will cook further even after being removed from the source of heat. Carryover cooking is often used as a finishing step in preparation of foods that are roasted or grilled, and should be accounted for in recipes as it can increase the internal temperature of foods by temperatures between 5 and 25 degrees Fahrenheit (3–14°C).

They can however provide upper bounds on the probability (or cross section) of pair production, as a function of energy. The ATLAS experiment at the Large Hadron Collider currently has the most stringent cross section limits for magnetic monopoles of 1 and 2 Dirac charges, produced through Drell-Yan pair production. A team led by Wendy Taylor searches for these particles based on theories that define them as long lived (they don't quickly decay), as well as being highly ionizing (their interaction with matter is predominantly ionizing). In 2019 the search for magnetic monopoles in the ATLAS detector reported its first results from data collected from the LHC Run 2 collisions at center of mass energy of 13 TeV, which at 34.4 fb−1 is the largest dataset analyzed to date.

The period depends on the length of the pendulum, and also to a slight degree on its weight distribution (the moment of inertia about its own center of mass) and the amplitude (width) of the pendulum's swing. For a point mass on a weightless string of length L swinging with an infinitesimally small amplitude, without resistance, the length of the string of a seconds pendulum is equal to L = g/π2 where g is the acceleration due to gravity, with units of length per second squared, and L is the length of the string in the same units. Using the SI recommended acceleration due to gravity of g0 = 9.80665 m/s2, the length of the string will be approximately 993.6 millimeters, i.e. less than a centimeter short of one meter everywhere on Earth.

The orbit of a long-period comet is properly obtained when the osculating orbit is computed at an epoch after leaving the planetary region and is calculated with respect to the center of mass of the solar system. Using JPL Horizons, the barycentric orbital elements for epoch 2030-Jan-01 generate a semi-major axis of 7,500 AU, an apoapsis distance of 15,000 AU, and a period of approximately 650,000 years. Before entering the planetary region (epoch 1950), C/2007 Q3 had a calculated barycentric orbital period of ~6.4 million years with an apoapsis (aphelion) distance of about 69,000 AU (1.09 light-years). The comet was probably in the outer Oort cloud for millions or billions of years with a loosely bound chaotic orbit until it was perturbed inward.

Intersecting Storage RingsThe ISR (standing for "Intersecting Storage Rings") was a particle accelerator at CERN. It was the world's first hadron collider, and ran from 1971 to 1984, with a maximum center of mass energy of 62 GeV. From its initial startup, the collider itself had the capability to produce particles like the J/ψ and the upsilon, as well as observable jet structure; however, the particle detector experiments were not configured to observe events with large momentum transverse to the beamline, leaving these discoveries to be made at other experiments in the mid-1970s. Nevertheless, the construction of the ISR involved many advances in accelerator physics, including the first use of stochastic cooling, and it held the record for luminosity at a hadron collider until surpassed by the Tevatron in 2004.

A muscle back is the more traditional design and consists of a solid metal head, typically made of forged iron. The design of the club typically distributes the metal more evenly around the clubhead (though most designs still place more weight along the sole of the club), which makes the center of mass of the club higher and the moment of inertia (the clubhead's resistance to rotation) lower as compared to newer cavity-backed designs. As such, these clubs are said to have a smaller "sweet spot", requiring greater skill and a more consistent swing to make accurate, straight shots. Novice golfers with less consistent swing fundamentals can easily mis-hit these clubs, causing shots to launch or curve off of the intended line of play (such as "pushing", "pulling", "slicing" or "hooking").

Accelerated Neutral Atoms Beams (ANAB) is a recent variation on GCIB . With ANAB the high velocity clusters are heated and evaporated by collisions with thermal energy gas molecules and the charged cluster remnants are deflected out of the beam leaving an intense focused beam of individual fast neutral monomers/atoms. The monomers are evaporated from the clusters with low thermal energies and they retain the center of mass velocity of the cluster and hence do not move out of the beam before colliding with the surface. When used to treat a surface, an ANAB beam has nearly the same total energy and velocity of the original GCIB beam but the smoothing effect on the surface is much different as the dispersed impacts of the individual fast atoms is more gentle than that of the clusters.

Newton was concerned to address the problem of how it is that we can experimentally determine the true motions of bodies in light of the fact that absolute space is not something that can be perceived. Such determination, he says, can be accomplished by observing the causes of motion (that is, forces) and not simply the apparent motions of bodies relative to one another (as in the bucket argument). As an example where causes can be observed, if two globes, floating in space, are connected by a cord, measuring the amount of tension in the cord, with no other clues to assess the situation, alone suffices to indicate how fast the two objects are revolving around the common center of mass. (This experiment involves observation of a force, the tension).

The rider's rear hand will often move further back on the boom to assist in proper placement of center of effort and sheeting-in later. Next, the board is jumped from the water, by straightening the rear leg, with the nose of the board commonly 45 degrees higher than the tail as it leaves the water. To assist rotation, and depending upon the desired initiation time of the rotation of the loop, the board may be carved (turned) downwind as it is jumped, and the bottom surface may be tilted about a longitudinal axis to expose it to the wind. To prepare for maximum speed of rotation, the rider next moves the center of effort of the sail as far away from their center of mass as possible.

Knowledge of the projectile drop and path has some practical uses to shooters even if it does not describe the actual trajectory of the projectile. For example, if the vertical projectile position over a certain range reach is within the vertical height of the target area the shooter wants to hit, the point of aim does not necessarily need to be adjusted over that range; the projectile is considered to have a sufficiently flat point-blank range trajectory for that particular target.Maximum Point Blank Range and the Battlesight Zero Also known as "battle zero", maximum point-blank range is also of importance to the military. Soldiers are instructed to fire at any target within this range by simply placing their weapon's sights on the center of mass of the enemy target.

Where one body is much more massive than the other (as is the case of an artificial satellite orbiting a planet), it is a convenient approximation to take the center of mass as coinciding with the center of the more massive body. Advances in Newtonian mechanics were then used to explore variations from the simple assumptions behind Kepler orbits, such as the perturbations due to other bodies, or the impact of spheroidal rather than spherical bodies. Lagrange (1736–1813) developed a new approach to Newtonian mechanics emphasizing energy more than force, and made progress on the three body problem, discovering the Lagrangian points. In a dramatic vindication of classical mechanics, in 1846 Urbain Le Verrier was able to predict the position of Neptune based on unexplained perturbations in the orbit of Uranus.

A C-start is a type of a very quick startle or escape reflex that is employed by fish and amphibians (including larval frogs and toads). There are two sequential stages in the C-start: first, the head rotates about the center of mass towards the direction of future escape, and the body of the animal exhibits a curvature that resembles a letter C; then, at the second stage, the animal is propelled forward. The duration of these stages varies from species to species from about 10 to 20 ms for the first stage, and from 20 to 30 ms for the second. In fish this forward propulsion does not require contraction of the antagonistic muscle, but results from the body stiffness and the hydrodynamic resistance of the tail.

The coordinate origin of WGS 84 is meant to be located at the Earth's center of mass; the uncertainty is believed to be less than 2 cm. The WGS 84 meridian of zero longitude is the IERS Reference Meridian,European Organisation for the Safety of Air Navigation and IfEN: WGS 84 Implementation Manual, p. 13. 1998 5.3 arc seconds or east of the Greenwich meridian at the latitude of the Royal Observatory. The WGS 84 datum surface is an oblate spheroid with equatorial radius a = m at the equator and flattening f = 1/. The refined value of the WGS 84 gravitational constant (mass of Earth’s atmosphere included) is GM = ×108 m³/s². The angular velocity of the Earth is defined to be ω = 72.92115×10−6 rad/s.

Balance Balance Training Since balance is a key predictor of recovery and is required in so many of our activities of daily living, it is often introduced into treatment plans by physiotherapists and occupational therapists when dealing with geriatrics, patients with neurological conditions, or others whom they have determined it to be beneficial. Balance training in stroke patients has been supported in the literature. Methods commonly used and proven to be effective for this population include sitting or standing balance practice with various progressions including reaching, variations in base of support, use of tilt boards, gait training varying speed, and stair climbing exercises. Another method to improve balance is perturbation training, which is an external force applied to a person's center of mass in an attempt to move it from the base of support.

To design a boat to deal with loads such that they do not shift in the modern world is rather simple. Most loads are in containers measuring 1/2, 1 or 2 TEUs, which are locked to each other and the deck with twist-locks, and occasionally reinforce the structures with steel cables. When containers become an issue with the stability of the boat, for example all the containers broke free and are hanging over the side shifting the center of mass, most ships will cut the containers loose and add extra ballast water to compensate. If objects fall around in containers, it isn't a huge deal unless they knock the container free, as container ships carry thousands of containers so having a couple with shifting loads, isn't a big deal.

In tree methods, such as a Barnes–Hut simulation, an octree is usually used to divide the volume into cubic cells and only interactions between particles from nearby cells need to be treated individually; particles in distant cells can be treated collectively as a single large particle centered at the distant cell's center of mass (or as a low-order multipole expansion). This can dramatically reduce the number of particle pair interactions that must be computed. To prevent the simulation from becoming swamped by computing particle-particle interactions, the cells must be refined to smaller cells in denser parts of the simulation which contain many particles per cell. For simulations where particles are not evenly distributed, the well-separated pair decomposition methods of Callahan and Kosaraju yield optimal O(n log n) time per iteration with fixed dimension.

In orbital mechanics, mean motion (represented by n) is the angular speed required for a body to complete one orbit, assuming constant speed in a circular orbit which completes in the same time as the variable speed, elliptical orbit of the actual body. The concept applies equally well to a small body revolving about a large, massive primary body or to two relatively same-sized bodies revolving about a common center of mass. While nominally a mean, and theoretically so in the case of two-body motion, in practice the mean motion is not typically an average over time for the orbits of real bodies, which only approximate the two-body assumption. It is rather the instantaneous value which satisfies the above conditions as calculated from the current gravitational and geometric circumstances of the body's constantly-changing, perturbed orbit.

It has been noted that the nervous system controls particular variables relevant to performance of a task, while leaving other variables free to vary; this is called the uncontrolled manifold hypothesis (UCM). The uncontrolled manifold is defined as the set of variables not affecting task performance; variables perpendicular to this set in Jacobian space are considered controlled variables (CM). For example, during a sit-to-stand task, head and center-of- mass position in the horizontal plane are more tightly controlled than other variables such as hand motion. Another study indicates that the quality of tongue's movements produced by bio-robots, which are controlled by a specially designed internal model, is practically uncorrelated with the stiffness of the tongue; in other words, during the speech production the relevant parameter is the quality of speech, while the stiffness is rather irrelevant.

On the other hand, if the center of mass height is behind or below the line, such as on most tandem bicycles or long-wheel-base recumbent bicycles, as well as cars, it is less likely that the front wheel can generate enough braking force to flip the bike. This means they can decelerate up to nearly the limit of adhesion of the tires to the road, which could reach 0.8 g if the coefficient of friction is 0.8, which is 40% more than an upright bicycle under even the best conditions. Bicycling Science author David Gordon Wilson points out that this puts upright bicyclists at particular risk of causing a rear-end collision if they tailgate cars. Similarly, powerful motorcycles can generate enough torque at the rear wheel to lift the front wheel off the ground in a maneuver called a wheelie.

Auto Union Type C The Auto Union Grand Prix racing cars types A to D were developed and built by a specialist racing department of Auto Union's Horch works in Zwickau, Germany, between 1933 and 1939. Of the 4 Auto Union racing cars, the Types A, B and C, used from 1934 to 1937 had supercharged V16 engines, and the final car, the Type D used in 1938 and 1939 (built to new 1938 regulations), had a supercharged 3L V12 that developed almost 550 horsepower. All of the designs were difficult to handle due to extreme power/weight ratios (wheelspin could be induced at over ), and marked oversteer due to uneven weight distribution (all models were tail heavy). The Type D was easier to drive because of its smaller, lower mass engine that was better positioned toward the vehicle's center of mass.

Through a number of modifications, the astronomical system of units now explicitly recognizes the consequences of general relativity, which is a necessary addition to the International System of Units in order to accurately treat astronomical data. The astronomical system of units is a tridimensional system, in that it defines units of length, mass and time. The associated astronomical constants also fix the different frames of reference that are needed to report observations. In particular, there is the barycentric celestial reference system (BCRS) centered at the barycenter of the Solar System, and the geocentric celestial reference system (GCRS) centered at the center of mass of the Earth (including its fluid envelopes) The system is a conventional system, in that neither the unit of length nor the unit of mass are true physical constants, and there are at least three different measures of time.

Starting in the late twentieth century, improved measurements of satellite orbits and star positions have provided extremely accurate determinations of the earth's center of mass and of its axis of revolution; and those parameters have been adopted also for all modern reference ellipsoids. The ellipsoid WGS-84, widely used for mapping and satellite navigation has close to 1/300 (more precisely, 1/298.257223563, by definition), corresponding to a difference of the major and minor semi-axes of approximately (more precisely, 21.3846858 km). For comparison, Earth's Moon is even less elliptical, with a flattening of less than 1/825, while Jupiter is visibly oblate at about 1/15 and one of Saturn's triaxial moons, Telesto, is highly flattened, with between 1/3 to 1/2 (meaning that the polar diameter is between 50% and 67% of the equatorial.

Cavity back style iron Cavity back, or perimeter weighted, irons are usually made by investment casting, which creates a harder metal allowing thinner surfaces while retaining durability, and also allows for more precise placement of metal than forging techniques. Cavity backs are so called because of the cavity created in the rear of the clubhead due to the removal of metal from the center of the clubhead's back, which is then redistributed, most of it very low and towards the toe and heel of the clubhead. This has the general effect of lowering the clubhead's center of mass, placing it underneath that of the ball allowing for a higher launch angle for a given loft. The perimeter weighting also increases the moment of inertia, making the clubhead more resistant to twisting on impact with the ball.

Fisher P-75A in flight Powered by a V-3420-19 24-cylinder engine rated at 2,600 hp driving co-axial contra-rotating propellers, the XP-75 flew for the first time on 17 November 1943. The second XP-75 flew shortly thereafter, with all six long-range XP-75s entering the test program by the spring 1944. The test program brought up numerous teething problems, including miscalculation of the fighter's center of mass, failure of the engine to produce its expected power, inadequate engine cooling, high aileron forces at high speed, and poor spin characteristics. Redesigns were introduced into the long-range XP-75s including a modified tail assembly, new "bubble" canopy, and a V-3420-23 engine that corrected most of the deficiencies by the time the first P-75A Eagles entered flight testing in September 1944.

Relation between proper motion and velocity components of an object. At emission, the object was at distance d from the Sun, and moved at angular rate μ radian/s, that is, μ = vt / d with vt = the component of velocity transverse to line of sight from the Sun. (The diagram illustrates an angle μ swept out in unit time at tangential velocity vt.) Proper motion is the astrometric measure of the observed changes in the apparent places of stars or other celestial objects in the sky, as seen from the center of mass of the Solar System, compared to the abstract background of the more distant stars. The components for proper motion in the equatorial coordinate system (of a given epoch, often J2000.0) are given in the direction of right ascension (μα) and of declination (μδ).

If the light source loses mass during the emission by E/c^2, the contradiction in the momentum law vanishes without the need of any compensating effect in the aether. Similar to Poincaré, Einstein concluded in 1906 that the inertia of (electromagnetic) energy is a necessary condition for the center of mass theorem to hold in systems, in which electromagnetic fields and matter are acting on each other. Based on the mass–energy equivalence, he showed that emission and absorption of em-radiation, and therefore the transport of inertia, solves all problems. On that occasion, Einstein referred to Poincaré's 1900-paper and wrote:Einstein (1906) Also Poincaré's rejection of the reaction principle due to the violation of the mass conservation law can be avoided through Einstein's E=mc^2, because mass conservation appears as a special case of the energy conservation law.

Artsutanov's concept was based on the linking of geosynchronous satellites to the ground with a cable. He suggested using the satellite as the base from which to construct the tower since a geosynchronous satellite will remain over a fixed point on the equator.The Navigator Quarterly News Letter (September 2002) By using a counterweight, a cable would be lowered from the geosynchronous orbit to the surface of Earth while the counterweight was extended from the satellite away from Earth, keeping the center of mass of the cable at the same height above the Earth. The ideas of Tsiolkovsky's compression-structure concept and Artsutanov's tension-structure concept differ in that a compression structure is well outside conceivable future capabilities, while the tension-structure is much easier to build and maintain, and is considered possible with near-future technologies.

The reason these points are in balance is that, at and , the distances to the two masses are equal. Accordingly, the gravitational forces from the two massive bodies are in the same ratio as the masses of the two bodies, and so the resultant force acts through the barycenter of the system; additionally, the geometry of the triangle ensures that the resultant acceleration is to the distance from the barycenter in the same ratio as for the two massive bodies. The barycenter being both the center of mass and center of rotation of the three-body system, this resultant force is exactly that required to keep the smaller body at the Lagrange point in orbital equilibrium with the other two larger bodies of system. (Indeed, the third body need not have negligible mass.) The general triangular configuration was discovered by Lagrange in work on the three-body problem.

The scheme was proposed both at Fermilab in the United States, and at CERN, and was ultimately adopted at CERN for the Super Proton Synchrotron (SPS). W and Z bosons are produced mainly as a result of quark-antiquark annihilation. In the parton model the momentum of a proton is shared between the proton's constituencies: a portion of the proton momentum is carried by the quarks, and the remainder by gluons. It will not be sufficient to accelerate protons to a momentum equal the mass of the boson, as each quark will only carry a portion of the momentum. To produce bosons in the estimated intervals of 60 to 80 GeV (W boson) and 75 to 92 GeV (Z boson), one would therefore need a proton- antiproton collider with a center-of-mass energy of approximately six times the boson masses, about 500-600 GeV.

The Foster is the standard American domestic shotgun slug; they are sometimes referred to as "American slugs" to differentiate them from the standard "European slug" design popularized earlier by Brenneke. Some sportswriters have consistently referred to these slugs as a "Forster" slugs, conflating the name with the Forster Brothers who manufactured reloading tools during the same time frame, so "Forster slug" is an alternate spelling that is commonly seen in the popular press of the 1930s for describing these slugs. The defining characteristic of the Foster slug is the deep hollow in the rear, which places the center of mass very near the front tip of the slug, much like a shuttlecock or a pellet from an airgun. If the slug begins to yaw in flight, drag will tend to push the lightweight rear of the slug back into straight flight, stabilizing the slug.

From the left, plumbata discarding sabot (#1); plumbata slugs (#2, #5); wad slug (#3), sabot slugs (#3, #4) A modern variant between the Foster slug and the sabot slug is the wad slug. This is a type of shotgun slug designed to be fired through a smoothbore shotgun barrel. Like the traditional Foster slug, a deep hollow is located in the rear of this slug, which serves to retain the center of mass near the front tip of the slug much like the Foster slug. However, unlike the Foster slug, a wad slug additionally has a key or web wall molded across the deep hollow, spanning the hollow, which serves to increase the structural integrity of the slug while also reducing the amount of expansion of the slug when fired, reducing the stress on the shot wad in which it rides down a barrel.

On September 30, 2009, the manufacturer Taser International issued a warning and new targeting guidelines to law enforcement agencies to aim shots below the chest center of mass as "avoiding chest shots with ECDs avoids the controversy about whether ECDs do or do not affect the human heart"TASER Law Enforcement Warnings Calgary Police Service indicated in a news interview that the rationale for the warning was "new medical research that is coming out is showing that the closer probe to heart distances have a likelihood, or a possibility, that they may affect the rhythm of the heart". Taser "recommended officers avoid tasing suspects in the chest area, citing the potential for cardiac arrests, lawsuits and effectiveness of the device". Central Texas Constable Richard McCain, whose deputy used a Taser weapon against an unarmed 72-year-old woman (resulting in a $40,000 lawsuit settlement), describes Taser's directive as "not really practical".

He was forced to bleed off some of his suit's pressure, in order to be able to bend the joints, eventually going below safety limits. Leonov did not report his action on the radio to avoid alarming others, but Soviet state radio and television had earlier stopped their live broadcasts from the spacecraft when the mission experienced difficulties. The two crew members subsequently experienced difficulty in sealing the hatch properly due to thermal distortion caused by Leonov's lengthy troubles returning to the craft, followed by a troublesome re-entry in which malfunction of the automatic landing system forced the use of its manual backup. The spacecraft was so cramped that the two cosmonauts, both wearing spacesuits, could not return to their seats to restore the ship's center of mass for 46 seconds after orienting the ship for reentry and a landing in Perm Krai.

In physics, potential energy is the energy held by an object because of its position relative to other objects, stresses within itself, its electric charge, or other factors. Common types of potential energy include the gravitational potential energy of an object that depends on its mass and its distance from the center of mass of another object, the elastic potential energy of an extended spring, and the electric potential energy of an electric charge in an electric field. The unit for energy in the International System of Units (SI) is the joule, which has the symbol J. The term potential energy was introduced by the 19th-century Scottish engineer and physicist William Rankine,William John Macquorn Rankine (1853) "On the general law of the transformation of energy," Proceedings of the Philosophical Society of Glasgow, vol. 3, no. 5, pages 276–280; reprinted in: (1) Philosophical Magazine, series 4, vol.

A fatigued or unconscious diver can be made to float face up at the surface by adjustment of their buoyancy and weights, so the buoyancy raises the top and front of the diver's body, and the weights act at the lower back of the body. An inflated horse-collar BC always provides this orientation, but an inflated vest or wing may float the diver face-down if the center of buoyancy is behind the centre of gravity. This floating orientation is generally considered undesirable and can be minimized by relocation of some of the weights further to the rear, and using higher density cylinders (typically steel), which also move the center of mass towards the back of the diver. The BC type can also be selected with this factor in mind, selecting a style with a center of buoyancy further forward when filled, as this has the same net effect.

If it is below the center of mass (CM) it will cause the beam to rotate counterclockwise around the CM and also cause the CM to move to the right. The center of percussion (CP) is below the CM. If the blow falls above the CP, the rightward translational motion will be bigger than the leftward rotational motion at P, causing the net initial motion of the fixture to be rightward. If the blow falls below the CP the opposite will occur, rotational motion at P will be larger than translational motion and the fixture will move initially leftward. Only if the blow falls exactly on the CP will the two components of motion cancel out to produce zero net initial movement at point P. When the sliding fixture is replaced with a pivot that cannot move left or right, an impulsive blow anywhere but at the CP results in an initial reactive force at the pivot.

Consider the parabola in the figure to the right. Pick two points on the parabola and call them A and B. right Suppose the line segment AC is parallel to the axis of symmetry of the parabola. Further suppose that the line segment BC lies on a line that is tangent to the parabola at B. The first proposition states: :The area of the triangle ABC is exactly three times the area bounded by the parabola and the secant line AB. :Proof: Let D be the midpoint of AC. Construct a line segment JB through D, where the distance from J to D is equal to the distance from B to D. We will think of the segment JB as a "lever" with D as its fulcrum. As Archimedes had previously shown, the center of mass of the triangle is at the point I on the "lever" where DI :DB = 1:3.

Conceptually, this is achieved by averaging the result of different FORM simulations. In practice, this is made possible by identifying the importance direction \boldsymbol \alpha in the input parameter space, which points towards the region which most strongly contributes to the overall failure probability. The importance direction can be closely related to the center of mass of the failure region, or to the failure point with the highest probability density, which often falls at the closest point to the origin of the limit state function, when the random variables of the problem have been transformed into the standard normal space. Once the importance direction has been set to point towards the failure region, samples are randomly generated from the standard normal space and lines are drawn parallel to the importance direction in order to compute the distance to the limit state function, which enables the probability of failure to be estimated for each sample.

There are many systems throughout the physical world that can be modeled as anharmonic oscillators in addition to the nonlinear mass-spring system. For example, an atom, which consists of a positively charged nucleus surrounded by a negatively charged electronic cloud, experiences a displacement between the center of mass of the nucleus and the electronic cloud when an electric field is present. The amount of that displacement, called the electric dipole moment, is related linearly to the applied field for small fields, but as the magnitude of the field is increased, the field-dipole moment relationship becomes nonlinear, just as in the mechanical system. Further examples of anharmonic oscillators include the large-angle pendulum; nonequilibrium semiconductors that possess a large hot carrier population, which exhibit nonlinear behaviors of various types related to the effective mass of the carriers; and ionospheric plasmas, which also exhibit nonlinear behavior based on the anharmonicity of the plasma.

The rotational inertia of the front wheel will lessen the severity of the wheel flop effect because it results in opposing torque being required to initiate or accelerate changing the direction of the front wheel. According to the equation listed above, increasing the trail and/or decreasing the head angle will increase the wheel flop factor on a bicycle or motorcycle, which will increase the torque required to bring the handlebars back to the straight ahead position and increase the vehicle's tendency to veer suddenly off the line of a curve. Also, increasing the weight borne by the front wheel of the vehicle, either by increasing the mass of the vehicle, rider and cargo or by changing the weight ratio to shift the center of mass forward, will increase the severity of the wheel flop effect. Increasing the rotational inertia of the front wheel by increasing the speed of the vehicle and the rotational speed of the wheel will tend to counter the wheel flop effect.

For example, the molar heat capacity of nitrogen at constant volume is 20.6 J⋅K−1⋅mol−1 (at 15 °C, 1 atm), which is 2.49 R.Steven T. Thornton and Andrew Rex (1993): Modern Physics for Scientists and Engineers, Saunders College Publishing, 1993 From the theoretical equation cV,m = fR, one concludes that each molecule has f = 5 degrees of freedom. These turn out to be three degrees of the molecule's velocity vector, plus two degrees from its rotation about an axis through the center of mass and perpendicular to the line of the two atoms. The degrees of freedom due to translations and rotations are called the rigid degrees of freedom, since they do not involve any deformation of the molecule. Because of those two extra degrees of freedom, the molar heat capacity cV,m of (20.6 J⋅K−1⋅mol−1) is greater than that of an hypothetical monoatomic gas (12.5 J⋅K−1⋅mol−1) by a factor of .

As mentioned above in the section on balance, one effect of turning the front wheel is a roll moment caused by gyroscopic precession. The magnitude of this moment is proportional to the moment of inertia of the front wheel, its spin rate (forward motion), the rate that the rider turns the front wheel by applying a torque to the handlebars, and the cosine of the angle between the steering axis and the vertical. For a sample motorcycle moving at 22 m/s (50 mph) that has a front wheel with a moment of inertia of 0.6 kg·m2, turning the front wheel one degree in half a second generates a roll moment of 3.5 N·m. In comparison, the lateral force on the front tire as it tracks out from under the motorcycle reaches a maximum of 50 N. This, acting on the 0.6 m (2 ft) height of the center of mass, generates a roll moment of 30 N·m.

In economics, Saari has shown that natural price mechanisms that set the rate of change of the price of a commodity proportional to its excess demand can lead to chaotic behavior rather than converging to an economic equilibrium, and has exhibited alternative price mechanisms that can be guaranteed to converge. However, as he also showed, such mechanisms require that the change in price be determined as a function of the whole system of prices and demands, rather than being reducible to a computation over pairs of commodities. In celestial mechanics, Saari's work on the -body problem "revived the singularity theory" of Henri Poincaré and Paul Painlevé, and proved Littlewood's conjecture that the initial conditions leading to collisions have measure zero. He also formulated the "Saari conjecture", that when a solution to the Newtonian -body problem has an unchanging moment of inertia relative to its center of mass, its bodies must be in relative equilibrium.

Poul Anderson, who had a degree in physics, worked out the physical framework for the anthology based on the characteristics of HD36395 as they were known in the early 1990s: one third of Earth Sun's mass, 82% of its diameter, spectral type M1 with a photosphere temperature of 3,400 K and a maximum emission in the near infrared. (The star is in fact very similar to Gliese 581, now known to have a planetary system.) The twin terrestrial planets are separated by an average distance of only 156,000 km (about 40% of the Earth-Moon distance). They orbit around their center of mass in 91 hours in locked rotation, which minimizes the effects of the huge tidal forces which they exert on each other. This constellation orbits Murasaki within the habitable zone, at a distance of only 0.223 astronomical units (sidereal year, 66 Earth days) where the planets receive about the same amount of total irradiation Mars gets from the Sun; however, with a spectral power distribution shifted to much longer wavelengths.

In the gravitational two-body problem, the orbits of the two bodies about each other are described by two overlapping conic sections with one of the foci of one being coincident with one of the foci of the other at the center of mass (barycenter) of the two bodies. Thus, for instance, the minor planet Pluto's largest moon Charon has an elliptical orbit which has one focus at the Pluto-Charon system's barycenter, which is a point that is in space between the two bodies; and Pluto also moves in an ellipse with one of its foci at that same barycenter between the bodies. Pluto's ellipse is entirely inside Charon's ellipse, as shown in this animation of the system. By comparison, the Earth's Moon moves in an ellipse with one of its foci at the barycenter of the Moon and the Earth, this barycenter being within the Earth itself, while the Earth (more precisely, its center) moves in an ellipse with one focus at that same barycenter within the Earth.

Prior to release of the vehicle stack for liftoff, the SRBs must simultaneously ignite and pressurize their combustion chambers and exhaust nozzles to produce a thrust derived, net counter-rotating moment exactly equal to the SSME's rotating moment. With the SRBs reaching full thrust, the hold-down bolts are blown, releasing the vehicle stack, the net rotating moment is zero, and the net vehicle thrust (opposing gravity) is positive, lifting the orbiter stack vertically from the launch pedestal, controllable through the coordinated gimbal movements of the SSMEs and the SRB exhaust nozzles. During ascent, multiple all-axis accelerometers detect and report the vehicle's flight and orientation (referencing the flight deck aboard the orbiter), as the flight reference computers translate navigation commands (steering to a particular waypoint in space, and at a particular time) into engine and motor nozzle gimbal commands, which orient the vehicle about its center of mass. As the forces on the vehicle change due to propellant consumption, increasing speed, changes in aerodynamic drag, and other factors, the vehicle automatically adjusts its orientation in response to its dynamic control command inputs.

193 Scientist James Richards from the University of Delaware stated that successful jumps depend upon "how much angular momentum do you leave the ice with, how small can you make your moment of inertia in the air, and how much time you can spend in the air". He found that many skaters, although they were able to gain the necessary angular momentum for takeoff, had difficulty gaining enough rotational speed to complete the jump. For example, a skater could successfully complete a jump by making small changes to his or her arm position partway through the rotation, and a small bend in the hips and knees allows a skater "to land with a lower center of mass than they started with, perhaps eking out a few precious degrees of rotation and a better body position for landing". A skater tends to spend the same amount of time in the air regardless of whether he or she completes triple or quadruple jumps, but his or her angular momentum at the start of triples and quadruples is slightly higher than it is for double jumps.

One effect of turning the front wheel is a roll moment caused by gyroscopic precession. The magnitude of this moment is proportional to the moment of inertia of the front wheel, its spin rate (forward motion), the rate that the rider turns the front wheel by applying a torque to the handlebars, and the cosine of the angle between the steering axis and the vertical. For a sample motorcycle moving at 22 m/s (50 mph) that has a front wheel with a moment of inertia of 0.6 kgm2, turning the front wheel one degree in half a second generates a roll moment of 3.5 Nm. In comparison, the lateral force on the front tire as it tracks out from under the motorcycle reaches a maximum of 50 N. This, acting on the 0.6 m (2 ft) height of the center of mass, generates a roll moment of 30 Nm. While the moment from gyroscopic forces is only 12% of this, it can play a significant part because it begins to act as soon as the rider applies the torque, instead of building up more slowly as the wheel out- tracks. This can be especially helpful in motorcycle racing.

The tendency of the clubs to correct mis- hits will frustrate a golfer's attempts to intentionally hit a curved shot (a "fade" or "draw"), for instance to avoid an obstacle lying along a straight flight path, or to counter a rightward or leftward slope to the fairway that would make a straight shot roll into the rough. This lack of ability to "work the ball" can frustrate a more skilled golfer attempting to place the ball more accurately on the fairway than a novice would normally be concerned with (the novice's primary concern being simply to keep the ball on the fairway in the first place). The increased clubhead mass and lower center of mass can also be incompatible with a more skilled player's stronger swing; the higher mass reduces clubhead speed, while the higher launch angle causes more backspin and wastes the golfer's energy sending the ball up into the air instead of out over the fairway. Clubs intended for skilled amateurs and professionals, while still incorporating some perimeter-weighting characteristics, generally have less extreme weight distribution, instead placing more weight closer to the center and higher, and reducing overall clubhead mass slightly.

Of course, the more energy that is used to excite the O2 vibrations, the less will be available for the recoil. REMPI of the O(1D) atom in conjunction with the product imaging technique provides an image that can be used to determine the O(1D) three-dimensional velocity distribution. A slice through this cylindrically symmetric distribution is shown in the figure, where an O(1D) atom that has zero velocity in the center-of-mass frame would arrive at the center of the figure. Note that there are four rings, corresponding to four main groups of O(1D) speeds. These correspond to production of the O2(1Δ) in the vibrational levels v = 0, 1, 2, and 3. The ring corresponding to v = 0 is the outer one, since production of the O2(1Δ) in this level leaves the most energy for recoil between the O(1D) and O2(1Δ). Thus, the product imaging technique immediately shows the vibrational distribution of the O2(1Δ). Note that the angular distribution of the O(1D) is not uniform – more of the atoms fly toward the north or south pole than to the equator.

Gauss' constant is derived from the application of Kepler's third law to the system of Earth+Moon and the Sun considered as a two body problem, relating the period of revolution () to the major semi-axis of the orbit () and the total mass of the orbiting bodies (). Its numerical value was obtained by setting the major semi-axis and the mass of the Sun to unity and measuring the period in mean solar days: : 2 / ( ) ≈ 0.0172021 [rad], where: : ≈ 365.256 [days], = (++) ≈ 1.00000304 [], and = 1 by definition. The value represents the mean angular motion of the Earth-Sun system, in radians per day, equivalent to a value just below one degree (the division of the circle into 360 degrees in Babylonian astronomy was likely intended as approximating the number of days in a solar yearDavid H. Kelley, Eugene F. Milone, Exploring Ancient Skies: A Survey of Ancient and Cultural Astronomy (2011), p. 219). The correction due to the division by the square root of reflects the fact that the Earth–Moon system is not orbiting the Sun itself, but the center of mass of the system.

The energy source is gravitational and results from a rain of gas falling onto the surface of the neutron star from a companion star or the interstellar medium. In 1974, Antony Hewish was awarded the Nobel Prize in Physics "for his decisive role in the discovery of pulsars" without Jocelyn Bell who shared in the discovery. In 1974, Joseph Taylor and Russell Hulse discovered the first binary pulsar, PSR B1913+16, which consists of two neutron stars (one seen as a pulsar) orbiting around their center of mass. Albert Einstein's general theory of relativity predicts that massive objects in short binary orbits should emit gravitational waves, and thus that their orbit should decay with time. This was indeed observed, precisely as general relativity predicts, and in 1993, Taylor and Hulse were awarded the Nobel Prize in Physics for this discovery. In 1982, Don Backer and colleagues discovered the first millisecond pulsar, PSR B1937+21. This object spins 642 times per second, a value that placed fundamental constraints on the mass and radius of neutron stars. Many millisecond pulsars were later discovered, but PSR B1937+21 remained the fastest-spinning known pulsar for 24 years, until PSR J1748-2446ad (which spins more than 700 times a second) was discovered.