505 Sentences With "reference frame" | Random Sentence Generator

However, that force-motion model only works in a non-accelerating reference frame (we call that an inertial reference frame).

The third edition of the International Celestial Reference Frame, or ICRF-1003, is the most up-to-date version of the International Astronomy Union's standardized reference frame.

This also encourages us to view from the reference frame of the runner.

That defines our "reference frame," from which we describe how the water is moving.

For a rotating reference frame, there are two fake forces we need to add.

So in the stationary reference frame, the balls appear to move in a straight line.

Here is a model of the motion of a water ball in the rotating reference frame.

It's standard to correct for this motion and to transform supernova data into a stationary reference frame.

But just for fun, what if we looked at it in the rotating reference frame of the sprinkler?

Which way is better, a non-rotating reference frame with real forces or a rotating frame with fake forces?

The ICRF-3 is the latest update to our reference frame, following ICRF-1 from 1998 and ICRF-2 from 2009.

The key to the Coriolis force is that it is always perpendicular to the object's velocity (in the rotating reference frame).

Awe then goes further and says, 'I want to know, but in order to know, I'm going to have to shift my reference frame.

Actually, there was no such force; your brain made it up to explain how you felt inside the accelerating reference frame of the car.

It's also OK if Russell Wilson thought it was a backward pass—because in the reference frame of the quarterback, it is a backward pass.

If we want to look at the water from the viewpoint of a rotating camera, that means that we now have an accelerating reference frame.

It depends on the observer's frame of reference, which is affected by things like their velocity and the strength of gravity within their reference frame.

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.

Wired explained it quite well:If you could just see the water from a stationary reference frame (maybe a floating hot air balloon), you would see the water indeed falling down.

This is a pretty amazing rise, but in the reference frame of the rest of the industry it could also signal a peculiar shift in mentality for how gaming companies are valued.

But from the reference frame of the rocket itself, it's not too different from pulling over to let a friend out before hitting the gas again and rolling on to the next destination.

"Historically, time was based on the mean rotation of the Earth relative to celestial bodies and the second was defined in this reference frame," Geoff Chester of the US Naval Observatory stated in the announcement.

Root AI's robots have multiple cameras (one on the arm of the robot itself, the "tool's" view, and one sitting to the side of the robot with a fixed reference frame) to collect both color images and 3D depth information.

Geocentric Celestial Reference Frame (GCRF) is the Earth-centered counterpart of the International Celestial Reference Frame.

The road serves as the reference frame, just as the earth serves as the reference frame for latitude and longitude.

Notice that the positive angle \theta above caused the arbitrary vector to rotate backwards when transitioned to the new DQ reference frame. In other words, its angle with respect to the new reference frame is less than its angle to the old reference frame. This is because the reference frame, not the vector, was rotated forwards. Actually, a forwards rotation of the reference frame is identical to a negative rotation of the vector.

A quantum reference frame is a reference frame which is treated quantum theoretically. It, like any reference frame, is an abstract coordinate system which defines physical quantities, such as time, position, momentum, spin, and so on. Because it is treated within the formalism of quantum theory, it has some interesting properties which do not exist in a normal classical reference frame.

As it is shown in the above, the amplitudes of the currents in the \alpha\beta\gamma reference frame are the same of that in the natural reference frame.

The egocentric reference frame refers to a proprioceptive reference frame using the position of an organism's body in a space. This reference frame relies heavily on somatosensory information, or feedback from the body's sensory system. Muscle vibrations can be used to alter a subject's perception of the location of their bodies by creating an abnormal somatosensory signal.

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.

Performing a rotation in an intrinsic reference frame is equivalent to right-multiplying its characteristic matrix (the matrix that has the vectors of the reference frame as columns) by the matrix of the rotation.

For the following formalism, the rotating frame of reference is regarded as a special case of a non-inertial reference frame that is rotating relative to an inertial reference frame denoted the stationary frame.

One of the profound consequences of relativity theory was the abolition of privileged reference frames. The description of physical phenomena should not depend upon who does the measuring - one reference frame should be as good as any other. Special relativity demonstrated that no inertial reference frame was preferential to any other inertial reference frame, but preferred inertial reference frames over noninertial reference frames. General relativity eliminated preference for inertial reference frames by showing that there is no preferred reference frame (inertial or not) for describing nature.

The allocentric reference frame describes a visual reference frame based on the arrangement of objects in an organism's environment. To test for the use of an allocentric reference frame, a "rod-and-frame" test, in which a subject's perception of virtual objects in an environment are altered, can be used to cause a body tilt as the subject believes to be correcting for the shift.

Please see Frame of reference for information about what a Reference Frame is.

So the longevity and the size of the reference frame are of quadratic relation in this particular case. In this spin-j system, the degradation is due to the loss of purity of the reference frame state. On the other hand, degradation can also be caused by misalignment of background reference. It has been shown, in such case, the longevity has a linear relation with the size of the reference frame.

Whereas for scalar- valued functions there is only a single possible reference frame, to take the derivative of a vector-valued function requires the choice of a reference frame (at least when a fixed Cartesian coordinate system is not implied as such). Once a reference frame has been chosen, the derivative of a vector- valued function can be computed using techniques similar to those for computing derivatives of scalar-valued functions. A different choice of reference frame will, in general, produce a different derivative function. The derivative functions in different reference frames have a specific kinematical relationship.

But the total energy of the system, including kinetic energy, fuel chemical energy, heat, etc., is conserved over time, regardless of the choice of reference frame. Different observers moving with different reference frames would however disagree on the value of this conserved energy. The kinetic energy of such systems depends on the choice of reference frame: the reference frame that gives the minimum value of that energy is the center of momentum frame, i.e.

A rotating frame of reference is a special case of a non-inertial reference frame that is rotating relative to an inertial reference frame. An everyday example of a rotating reference frame is the surface of the Earth. (This article considers only frames rotating about a fixed axis. For more general rotations, see Euler angles.) In the inertial frame of reference (upper part of the picture), the black ball moves in a straight line.

The African Geodetic Reference Frame (AFREF) is a project designed to unify the many geodetic reference frames of Africa using data from a network of permanent Global Navigation Satellite Systems (GNSS) stations as the primary data source for the implementation of a uniform reference frame.

A terrestrial reference frame is the reference frame as one views from earth, or from the ground of another earth-like body. A terrestrial reference frame affects the way we perceive almost everything from day to day because as we live on the earth an earth point of view is the only type we can experience. The most noticeable result of the Terrestrial Reference Frame (TRF) is the way the sun appears to be rising and setting in the sky everyday, when in actuality it is the earth rotating on its axis. Our point of view is in essence distorted by the place in which we view it happening.

It is larger by a factor of . The arbitrary vector did not change magnitude through this conversion from the ABC reference frame to the XYZ reference frame (i.e., the sphere did not change size). This is true for the power-invariant form of the Clarke transform.

Two most widely used transformation methods are dqo (or qdo or odq or simply d-q) transformation and αβϒ (or α-β) transformation. In d-q transformation the three phase quantities of machine in the abc reference frame is referred to d-q reference frame. Transformation equation has the general form [Fdqo] = [K][Fabc], where K is the transformation matrix, for detail refer Dqo transformation. The d-q reference frame may be stationary or rotating at certain angular speed.

The difference between P-frames and B-frames is the reference frame they are allowed to use.

The dqo transform is conceptually similar to the αβγ transform. Whereas the dqo transform is the projection of the phase quantities onto a rotating two-axis reference frame, the αβγ transform can be thought of as the projection of the phase quantities onto a stationary two-axis reference frame.

In most such situations, the same laws of physics can be used if certain predictable fictitious forces are added into consideration; an example is a uniformly rotating reference frame, which can be treated as an inertial reference frame if one adds a fictitious centrifugal force and Coriolis force into consideration. The problems involved are not always so trivial. Special relativity predicts that an observer in an inertial reference frame doesn't see objects he would describe as moving faster than the speed of light. However, in the non-inertial reference frame of Earth, treating a spot on the Earth as a fixed point, the stars are observed to move in the sky, circling once about the Earth per day.

These rotations are intrinsic rotations and the calculus behind them is similar to the Frenet- Serret formulas. Performing a rotation in an intrinsic reference frame is equivalent to right-multiply its characteristic matrix (the matrix that has the vector of the reference frame as columns) by the matrix of the rotation.

Reconsidering the problem at the very beginning, one can certainly find a flaw of ambiguity in it, but it is generally understood that a standard reference frame is implicitly used in the problem. In fact, when a reference frame is classical, whether or not including it in the physical description of a system is irrelevant. One will get the same prediction by treating the reference frame internally or externally. To illustrate the point further, a simple system with a ball bouncing off a wall is used.

The dq0 transform is conceptually similar to the \alpha\beta\gamma transform. Whereas the dq0 transform is the projection of the phase quantities onto a rotating two-axis reference frame, the \alpha\beta\gamma transform can be thought of as the projection of the phase quantities onto a stationary two-axis reference frame.

The solution was constrained to be consistent with the International Terrestrial Reference Frame (ITRF2008) and earth orientation parameters (EOP) systems.

In relativistic physics, the coordinates of a hyperbolically accelerated reference frame constitute an important and useful coordinate chart representing part of flat Minkowski spacetime. In special relativity, a uniformly accelerating particle undergoes hyperbolic motion, for which a uniformly accelerating frame of reference in which it is at rest can be chosen as its proper reference frame. The phenomena in this hyperbolically accelerated frame can be compared to effects arising in a homogeneous gravitational field. For general overview of accelerations in flat spacetime, see Acceleration (special relativity) and Proper reference frame (flat spacetime).

Therefore, the same acceleration acts upon both the dart and the monkey throughout the fall. Transform the reference frame to one that is accelerated upward by the amount with respect to the Earth's reference frame (which is to say the acceleration of the new frame with respect to the Earth is ). Because of Galilean equivalence, the (approximately) constant gravitational field (approximately) disappears, leaving us with only the horizontal velocity of both the dart and the monkey. In this reference frame the hunter should aim straight at the monkey, since the monkey is stationary.

The term observer in special relativity refers most commonly to an inertial reference frame. In such cases an inertial reference frame may be called an "inertial observer" to avoid ambiguity. Note that these uses differ significantly from the ordinary English meaning of "observer". Reference frames are inherently nonlocal constructs, covering all of space and time or a nontrivial part of it; thus it does not make sense to speak of an observer (in the special relativistic sense) having a location, except for denoting the origin of his reference frame.

Einstein's equivalence principle generalizes this analogy, stating that an accelerating reference frame is locally indistinguishable from an inertial reference frame with a gravity force acting upon it. In this way, the Gravity Probe A was a test of the equivalence principle, matching the observations in the inertial reference frame (of special relativity) of the Earth's surface affected by gravity, with the predictions of special relativity for the same frame treated as being accelerating upwards with respect to free fall reference, which can thought of being inertial and gravity-less.

An inertial reference frame (or inertial frame in short) is a frame in which all the physical laws hold. For instance, in a rotating reference frame, Newton's laws have to be modified because there is an extra Coriolis force (such frame is an example of non-inertial frame). Here, "rotating" means "rotating with respect to some inertial frame". Therefore, although it is true that a reference frame can always be chosen to be any physical system for convenience, any system has to be eventually described by an inertial frame, directly or indirectly.

P-frames provide more compression than I-frames because they take advantage of the data in a previous I-frame or P-frame – a reference frame. To generate a P-frame, the previous reference frame is reconstructed, just as it would be in a TV receiver or DVD player. The frame being compressed is divided into 16 pixel by 16 pixel macroblocks. Then, for each of those macroblocks, the reconstructed reference frame is searched to find a 16 by 16 area that closely matches the content of the macroblock being compressed.

Instead of inertial frames, these accelerated motions and curved worldlines can also be described using accelerated or curvilinear coordinates. The proper reference frame established that way is closely related to Fermi coordinates.Misner & Thorne & Wheeler (1973), Section 6Gourgoulhon (2013), entire book For instance, the coordinates for an hyperbolically accelerated reference frame are sometimes called Rindler coordinates, or those of a uniformly rotating reference frame are called rotating cylindrical coordinates (or sometimes Born coordinates). In terms of the equivalence principle, the effects arising in these accelerated frames are analogous to effects in a homogeneous, fictitious gravitational field.

It makes possible to uniquely determine canonical momenta of the particle and forces acting on it in a given reference frame.

The effects of special relativity occur whether or not there is a sentient being within the inertial reference frame to witness them.

The modern interpretation is that centrifugal force in a rotating reference frame is a pseudo-force that appears in equations of motion in rotating frames of reference, to explain effects of inertia as seen in such frames. Leibniz's centrifugal force may be understood as an application of this conception, as a result of his viewing the motion of a planet along the radius vector, that is, from the standpoint of a special reference frame rotating with the planet. Leibniz introduced the notions of vis viva (kinetic energy) and action, which eventually found full expression in the Lagrangian formulation of mechanics. In deriving Leibniz's radial equation from the Lagrangian standpoint, a rotating reference frame is not used explicitly, but the result is equivalent to that found using Newtonian vector mechanics in a co-rotating reference frame.

Motion of the Solar System's barycenter relative to the Sun As many of the objects listed below have some of the most extreme orbits of any objects in the Solar System, describing their orbit precisely can be particularly difficult. For most objects in the Solar System, a heliocentric reference frame (relative to the gravitational center of the Sun) is sufficient to explain their orbits. However, as the orbits of objects become closer to the Solar System's escape velocity, with long orbital periods on the order of hundreds or thousands of years, a different reference frame is required to describe their orbit: a barycentric reference frame. A barycentric reference frame measures the asteroid's orbit relative to the gravitational center of the entire Solar System, rather than just the Sun.

In general the position and orientation in space of a rigid body are defined as the position and orientation, relative to the main reference frame, of another reference frame, which is fixed relative to the body, and hence translates and rotates with it (the body's local reference frame, or local coordinate system). At least three independent values are needed to describe the orientation of this local frame. Three other values describe the position of a point on the object. All the points of the body change their position during a rotation except for those lying on the rotation axis.

The defining extragalactic reference frame of the ICRS is the International Celestial Reference Frame (currently ICRF3) based on hundreds of extra- galactic radio sources, mostly quasars, distributed around the entire sky. Because they are so distant, they are apparently stationary to our current technology, yet their positions can be measured with the utmost accuracy by Very Long Baseline Interferometry (VLBI). The positions of most are known to 0.001 arcsecond or better. At optical wavelengths, the ICRS is currently realized by the Hipparcos Celestial Reference Frame (HCRF), a subset of about 100,000 stars in the Hipparcos Catalogue.

The objective of the Gravity Probe A experiment was to test the validity of the equivalence principle. The equivalence principle is a key component of Albert Einstein's theory of general relativity, and states that the laws of physics are the same in an accelerating reference frame as they are in a reference frame that is acted upon by a uniform gravitational field.

Then a head-centered reference frame is identical to a world-centered reference frame. Or colloquially, the eye-in-head position directly determines the gaze direction. Some results are available on human eye movements under natural conditions where head movements are allowed as well. The relative position of eye and head, even with constant gaze direction, influences neuronal activity in higher visual areas.

Moreover, a reference frame where the Christoffel symbols are zero can be applicable only at a point, it is unapplicable to a finite region.

If a global reference frame (such as WGS84, for example) is used, the longitude of a place on the surface will change from year to year. To minimize this change, when dealing just with points on a single plate, a different reference frame can be used, whose coordinates are fixed to a particular plate, such as "NAD83" for North America or "ETRS89" for Europe.

However the total energy of an isolated system, i.e. one in which energy can neither enter nor leave, does not change over time in the reference frame in which it is measured. Thus, the chemical energy converted to kinetic energy by a rocket engine is divided differently between the rocket ship and its exhaust stream depending upon the chosen reference frame. This is called the Oberth effect.

Maxwell's equations are exactly consistent with special relativity—i.e., if they are valid in one inertial reference frame, then they are automatically valid in every other inertial reference frame. In fact, Maxwell's equations were crucial in the historical development of special relativity. However, in the usual formulation of Maxwell's equations, their consistency with special relativity is not obvious; it can only be proven by a laborious calculation.

Polar motion in arc-seconds as function of time in days (0.1 arcsec ≈ 3 meters). Polar motion of the Earth is the motion of the Earth's rotational axis relative to its crust. This is measured with respect to a reference frame in which the solid Earth is fixed (a so-called Earth-centered, Earth-fixed or ECEF reference frame). This variation is only a few meters.

Hafnium/tungsten (Hf/W) isotopic ratios, when compared with a chondritic reference frame, show a marked enrichment in the silicate earth indicating depletion in Earth's core. Iron meteorites, believed to be resultant from very early core fractionation processes, are also depleted. Niobium/tantalum (Nb/Ta) isotopic ratios, when compared with a chondritic reference frame, show mild depletion in bulk silicate Earth and the moon.

In physics, a frame of reference (or reference frame) consists of an abstract coordinate system and the set of physical reference points that uniquely fix (locate and orient) the coordinate system and standardize measurements within that frame. For n dimensions, reference points are sufficient to fully define a reference frame. Using rectangular (Cartesian) coordinates, a reference frame may be defined with a reference point at the origin and a reference point at one unit distance along each of the n coordinate axes. In Einsteinian relativity, reference frames are used to specify the relationship between a moving observer and the phenomenon or phenomena under observation.

A proper reference frame in the theory of relativity is a particular form of accelerated reference frame, that is, a reference frame in which an accelerated observer can be considered as being at rest. It can describe phenomena in curved spacetime, as well as in "flat" Minkowski spacetime in which the spacetime curvature caused by the energy-momentum tensor can be disregarded. Since this article considers only flat spacetime—and uses the definition that special relativity is the theory of flat spacetime while general relativity is a theory of gravitation in terms of curved spacetime—it is consequently concerned with accelerated frames in special relativity.Misner & Thorne & Wheeler (1973), p.

Magnetic field lines can be clearly visualized by sprinkling iron filings over a bar magnet. The modern (post-Einstein) interpretation is that the magnetic field is equivalent to the electric field, but in a different reference frame. Since magnetic fields can be interpreted as electric fields in a different reference frame (and vice versa), special relativity connects the two fields. One postulate of special relativity is length contraction, and because of that, the charge density in the wire increases, so a current-carrying wire viewed in a moving reference frame experiences a length-contracted coulomb force as compared to the wire in a stationary frame.

This simple problem illustrates the importance of a reference frame: a reference frame is quintessential in a clear description of a system, whether it is included implicitly or explicitly. When speaking of a car moving towards east, one is referring to a particular point on the surface of the Earth; moreover, as the Earth is rotating, the car is actually moving towards a changing direction, with respect to the Sun. In fact, this is the best one can do: describing a system in relation to some reference frame. Describing a system with respect to an absolute space does not make much sense because an absolute space, if it exists, is unobservable.

In astrometry, an International Celestial Reference Frame (ICRF) is a realization of the International Celestial Reference System (ICRS) using reference celestial sources observed at radio wavelengths. In the context of the ICRS, a reference frame is the physical realization of a reference system, i.e., the reference frame is the set of reported coordinates of the reference sources, with the coordinates derived using the procedures spelled out by the ICRS. The ICRF creates a quasi-inertial frame of reference centered at the barycenter of the Solar System, whose axes are defined by the measured positions of extragalactic sources (mainly quasars) observed using very long baseline interferometry.

Towards the right stalling will decrease whereas it will increase towards its left. Movement of the rotating stall can be observed depending upon the chosen reference frame.

In the reference frame of the interface between two surfaces, static friction does no work, because there is never displacement between the surfaces. In the same reference frame, kinetic friction is always in the direction opposite the motion, and does negative work. However, friction can do positive work in certain frames of reference. One can see this by placing a heavy box on a rug, then pulling on the rug quickly.

Turning forces are generated during maneuvers for balancing in addition to just changing direction of travel. These may be interpreted as centrifugal forces in the accelerating reference frame of the bike and rider; or simply as inertia in a stationary, inertial reference frame and not forces at all. Gyroscopic forces acting on rotating parts such as wheels, engine, transmission, etc., are also due to the inertia of those rotating parts.

In this context, the phrase often becomes "observational frame of reference" (or "observational reference frame"), which implies that the observer is at rest in the frame, although not necessarily located at its origin. A relativistic reference frame includes (or implies) the coordinate time, which does not equate across different frames moving relatively to each other. The situation thus differs from Galilean relativity, where all possible coordinate times are essentially equivalent.

Quasi-satellite orbit of in the year 2589, looking vertically down on the ecliptic. Left, orbits of Asteroid and Earth in the reference frame of the fixed stars; right, in the reference frame of the Earth–Sun system. Image: JPL Because of its orbital inclination of 10.739° to the ecliptic, is not always forced by the Earth on its horseshoe orbit however but can sometimes slip out of this pattern.

In special relativity, an observer is a frame of reference from which a set of objects or events are being measured. Usually this is an inertial reference frame or "inertial observer". Less often an observer may be an arbitrary non- inertial reference frame such as a Rindler frame which may be called an "accelerating observer". The special relativity usage differs significantly from the ordinary English meaning of "observer".

The proper time of objects within a gravity well will pass more slowly than the coordinate time even when they are at rest with respect to the coordinate reference frame. Gravitational as well as motional time dilation must be considered for each object of interest, and the effects are functions of the velocity relative to the reference frame and of the gravitational potential as indicated in (). There are four purpose-designed coordinate time scales defined by the IAU for use in astronomy. Barycentric Coordinate Time (TCB) is based on a reference frame comoving with the barycenter of the Solar system, and has been defined for use in calculating motion of bodies within the Solar system.

Therefore, the dart will always hit the monkey, no matter the initial speed of the dart, no matter the acceleration of gravity. Another way of looking at the problem is by a transformation of the reference frame. Earlier the problem was stated in a reference frame in which the Earth is motionless. However, for very small distances on the surface of Earth the acceleration due to gravity can be considered constant to good approximation.

The geocentric reference frame involves visual inputs to help detect the verticality of an environment through gravitational pull. The sole of the foot contains receptors in the skin to detect the force of gravity, and plays a large role in standing or walking balance. The abdominal organs also contain receptors that provide geocentric information. "Roll-tilt" tests in which a subject's body is mechanically moved can be used to test for geocentric reference frame function.

In classical mechanics, the Euler force is the fictitious tangential force that appears when a non-uniformly rotating reference frame is used for analysis of motion and there is variation in the angular velocity of the reference frame's axes. The Euler acceleration (named for Leonhard Euler), also known as azimuthal acceleration or transverse acceleration is that part of the absolute acceleration that is caused by the variation in the angular velocity of the reference frame.

Relative velocity is a measurement of velocity between two objects as determined in a single coordinate system. Relative velocity is fundamental in both classical and modern physics, since many systems in physics deal with the relative motion of two or more particles. In Newtonian mechanics, the relative velocity is independent of the chosen inertial reference frame. This is not the case anymore with special relativity in which velocities depend on the choice of reference frame.

Inertial navigation systems are used in many different moving objects. However, their cost and complexity place constraints on the environments in which they are practical for use. Gyroscopes measure the angular velocity of the sensor frame with respect to the inertial reference frame. By using the original orientation of the system in the inertial reference frame as the initial condition and integrating the angular velocity, the system's current orientation is known at all times.

Mostly due to the influence of the outer gas giants, the Solar System barycenter varies by up to twice the radius of the Sun. This difference in position can lead to significant changes in the orbits of long-period comets and distant asteroids. Many comets have hyperbolic (unbound) orbits in a heliocentric reference frame, but in a barycentric reference frame have much more firmly bound orbits, with only a small handful remaining truly hyperbolic.

When possible, fluid dynamicists try to find a reference frame in which the flow is steady, so that they can use experimental methods of creating streaklines to identify the streamlines.

The helicity of a particle is the direction of its spin relative to its momentum; particles with spin in the same direction as their momentum are called right-handed and they are otherwise called left-handed. When a particle is massless, the direction of its momentum relative to its spin is the same in every reference frame, whereas for massive particles it is possible to 'overtake' the particle by choosing a faster-moving reference frame; in the faster frame, the helicity is reversed. Chirality is a technical property, defined through transformation behaviour under the Poincaré group, that does not change with reference frame. It is contrived to agrees with helicity for massless particles, and is still well defined for particles with mass.

Assume the second postulate of special relativity stating the constancy of the speed of light, independent of reference frame, and consider a collection of reference systems moving with respect to each other with constant velocity, i.e. inertial systems, each endowed with its own set of Cartesian coordinates labeling the points, i.e. events of spacetime. To express the invariance of the speed of light in mathematical form, fix two events in spacetime, to be recorded in each reference frame.

Streamlines are frame-dependent. That is, the streamlines observed in one inertial reference frame are different from those observed in another inertial reference frame. For instance, the streamlines in the air around an aircraft wing are defined differently for the passengers in the aircraft than for an observer on the ground. In the aircraft example, the observer on the ground will observe unsteady flow, and the observers in the aircraft will observe steady flow, with constant streamlines.

In physics, the relativity of simultaneity is the concept that distant simultaneity – whether two spatially separated events occur at the same time – is not absolute, but depends on the observer's reference frame.

The transformation from a reference frame 1 to a reference frame 2 can be described with three translations Δx, Δy, Δz, three rotations Rx, Ry, Rz and a scale parameter μ. The Helmert transformation (named after Friedrich Robert Helmert, 1843-1917) is a transformation method within a three-dimensional space. It is frequently used in geodesy to produce distortion-free transformations from one datum to another. The Helmert transformation is also called a seven-parameter transformation and is a similarity transformation.

This suggests, that route knowledge, which is supported by direct navigation, is more likey to be encoded within an egocentric reference frame and survey knowledge, which is supported by map learning, to be more likely to be encoded within an allocentric reference frame in turn. Whilst spatial information can be stored into these different frames, they already seem to develop together in early stages of childhood and appear to be necessarily used in combination in order to solve everyday life tasks.

The train-and-platform experiment from the reference frame of an observer on board the train Reference frame of an observer standing on the platform (length contraction not depicted) A popular picture for understanding this idea is provided by a thought experiment similar to those suggested by Daniel Frost Comstock in 1910The thought experiment by Comstock described two platforms in relative motion. See: . and Einstein in 1917.Einstein's thought experiment used two light rays starting at both ends of the platform.

Regional Reference Frame Sub-Commission for Europe (EUREF) is the sub- commission of the International Association of Geodesy (IAG), part of the Sub- Commission 1.3 (Regional Reference Frames), under IAG Commission 1 (Reference Frames). EUREF deals with the definition, realization and maintenance of the European Geodetic Reference Frame. The goal of EUREF is to establish a unified geodetic datum (ETRS89) and a consistent network of reference stations (EPN) throughout Europe. EUREF was founded in 1987 at the IUGG General Assembly held in Vancouver.

Viewed from a non-rotating reference frame (i.e. not one rotating with the Earth) and ignoring the forces of gravity and air resistance, a projectile moves in a straight line. When viewed from a reference frame fixed with respect to the Earth, that straight trajectory appears to curve sideways. The direction of this horizontal curvature is to the right in the northern hemisphere and to the left in the southern hemisphere, and does not depend on the azimuth of the shot.

For this reason, to simplify the description of Earth's orientation in astronomy and geodesy, it was conventional to chart the positions of the stars in the sky according to right ascension and declination, which are based on a frame that follows Earth's precession, and to keep track of Earth's rotation, through sidereal time, relative to this frame as well. In this reference frame, Earth's rotation is close to constant, but the stars appear to rotate slowly with a period of about 25,800 years. It is also in this reference frame that the tropical year, the year related to Earth's seasons, represents one orbit of Earth around the Sun. The precise definition of a sidereal day is the time taken for one rotation of Earth in this precessing reference frame.

Woelfel, J., & Barnett, G. A. (1992). "Procedures for controlling reference frame effects in the measurement of multidimensional processes." Quality and Quantity, 26, 367–381. Woelfel, J., Barnett, G. A., Pruzek, R., Zimmelman, R. (1989).

DE402 introduced coordinates referred to the International Celestial Reference Frame (ICRF). The JPL ephemerides have been the basis of the Astronomical Almanac since 1981's DE200. The current (2018) Almanac is derived from DE430.

Misorientation is the difference in crystallographic orientation between two crystallites in a polycrystalline material. In crystalline materials, the orientation of a crystallite is defined by a transformation from a sample reference frame (i.e. defined by the direction of a rolling or extrusion process and two orthogonal directions) to the local reference frame of the crystalline lattice, as defined by the basis of the unit cell. In the same way, misorientation is the transformation necessary to move from one local crystal frame to some other crystal frame.

Euler angles, one of the possible ways to describe an orientation The first attempt to represent an orientation was owed to Leonhard Euler. He imagined three reference frames that could rotate one around the other, and realized that by starting with a fixed reference frame and performing three rotations, he could get any other reference frame in the space (using two rotations to fix the vertical axis and another to fix the other two axes). The values of these three rotations are called Euler angles.

Because of the bending of spacetime, an observer on Earth (in a lower gravitational potential) should measure a slower rate at which time passes than an observer that is higher in altitude (at higher gravitational potential). This effect is known as gravitational time dilation. The experiment was a test of a major consequence of Einstein's general relativity, the equivalence principle. The equivalence principle states that a reference frame in a uniform gravitational field is indistinguishable from a reference frame that is under uniform acceleration.

The surface of the Earth is a rotating reference frame. To solve classical mechanics problems exactly in an Earth-bound reference frame, three fictitious forces must be introduced: the Coriolis force, the centrifugal force (described below) and the Euler force. The Euler force is typically ignored because the variations in the angular velocity of the rotating Earth surface are usually insignificant. Both of the other fictitious forces are weak compared to most typical forces in everyday life, but they can be detected under careful conditions.

It is this entropy coded data that is broadcast or that is put on DVDs. In the receiver or the player, the whole process is reversed, enabling the receiver to reconstruct, to a close approximation, the original frame. The processing of B-frames is similar to that of P-frames except that B-frames use the picture in a subsequent reference frame as well as the picture in a preceding reference frame. As a result, B-frames usually provide more compression than P-frames.

The resulting Hipparcos reference frame is thus a materialisation of the ICRS in the optical. It extends and improves the J2000 (FK5) system, retaining approximately the global orientation of that system but without its regional errors.

As viewed from Earth it would take about , or times the current age of the universe, for a photon to gain a 1 cm lead over a Planck energy proton as observed in Earth's reference frame.

In order to infer that the labeled mass values are correct, an object must be hung from the spring balance at rest in an inertial reference frame, interacting with no other objects but the scale itself.

In exploring the equivalence of gravity and acceleration as well as the role of tidal forces, Einstein discovered several analogies with the geometry of surfaces. An example is the transition from an inertial reference frame (in which free particles coast along straight paths at constant speeds) to a rotating reference frame (in which extra terms corresponding to fictitious forces have to be introduced in order to explain particle motion): this is analogous to the transition from a Cartesian coordinate system (in which the coordinate lines are straight lines) to a curved coordinate system (where coordinate lines need not be straight). A deeper analogy relates tidal forces with a property of surfaces called curvature. For gravitational fields, the absence or presence of tidal forces determines whether or not the influence of gravity can be eliminated by choosing a freely falling reference frame.

An inclination of zero ensures that the orbit remains over the equator at all times, making it stationary with respect to latitude from the point of view of a ground observer (and in the ECEF reference frame).

The general principle of relativity states: That is, physical laws are the same in all reference frames—inertial or non-inertial. An accelerated charged particle might emit synchrotron radiation, though a particle at rest doesn't. If we consider now the same accelerated charged particle in its non-inertial rest frame, it emits radiation at rest. Physics in non-inertial reference frames was historically treated by a coordinate transformation, first, to an inertial reference frame, performing the necessary calculations therein, and using another to return to the non-inertial reference frame.

Plate motions, both those observable now and in the past, are referred ideally to a reference frame that allows other plate motions to be calculated. For example, a central plate, such as the African plate, may have the motions of adjacent plates referred to it. By composition of reconstructions, additional plates can be reconstructed to the central plate. In turn, the reference plate may be reconstructed, together with the other plates, to another reference frame, such as the earth's magnetic field, as determined from paleomagnetic measurements of rocks of known age.

Further, the equivalence principle predicts that phenomenon of different time flow rates, present in a uniformly accelerating reference frame, will also be present in a stationary reference frame that is in a uniform gravitational field. The probe was launched on June 18, 1976 from the NASA-Wallops Flight Center in Wallops Island, Virginia. The probe was carried via a Scout rocket, and attained a height of , while remaining in space for 1 hour and 55 minutes, as intended. It returned to Earth by splashing down into the Atlantic Ocean.

In a reference frame rotating about an axis through its origin, all objects, regardless of their state of motion, appear to be under the influence of a radially (from the axis of rotation) outward force that is proportional to their mass, to the distance from the axis of rotation of the frame, and to the square of the angular velocity of the frame.Feynman Lectures on Physics, Book 1, 12-11. This is the centrifugal force. As humans usually experience centrifugal force from within the rotating reference frame, e.g.

Humphreys' book Starlight and Time presents his alternative to the Big Bang in an attempt to solve what young Earth creationists call the Distant Starlight Problem. Its thesis is that the Earth and universe are about six thousand years old when measured in Earth's reference frame, whereas the outer edge of an expanding and rotating 3-dimensional universe is billions of years old (as measured from its reference frame). It proposes, using the principles of relativity, to postulate that time ticked at different rates during the universe's origin.Starlight and Time, Russell Humphreys, Chapter 2, p.

The Hipparcos Celestial Reference Frame (HCRF) was a reference frame similar to ICRF, but earlier, used in association with the Hipparcos satellite, which functioned between 1989 and 1993. That satellite took copious stellar parallax measurements at accuracies exceeding anything otherwise available at the time, thus producing a catalog of stars still in wide use today. No such extensive mapping has yet been completed based upon subsequent improvements in measurement capability. With lower precision then, and at optical wavelengths, the ICRS and BCRS can also be specified using the HCRF.

Any such term must be both gauge and reference-frame invariant, otherwise the laws of physics would depend on an arbitrary choice or the frame of an observer. Therefore, the global Poincaré symmetry, consisting of translational symmetry, rotational symmetry and the inertial reference frame invariance central to the theory of special relativity must apply. The local gauge symmetry is the internal symmetry. The three factors of the gauge symmetry together give rise to the three fundamental interactions, after some appropriate relations have been defined, as we shall see.

In this form the equations of motion carry an explicit time dependence through the coordinates x_i(t), y_i(t). However, this time-dependence can be removed through a transformation to a rotating reference frame, which simplifies any subsequent analysis.

Rotating-frame depiction of the horseshoe exchange orbits of Janus and Epimetheus Animation of Epimetheus orbit - Rotating reference frame Objects in a horseshoe orbit librate around 180° from the primary. Their orbits encompass both equilateral Lagrangian points, i.e. and .

Frames that use prediction from a single preceding reference frame (or a single frame for prediction of each region) are called P-frames. B-frames use prediction from a (possibly weighted) average of two reference frames, one preceding and one succeeding.

The International Earth Rotation and Reference Systems Service (IERS), formerly the International Earth Rotation Service, is the body responsible for maintaining global time and reference frame standards, notably through its Earth Orientation Parameter (EOP) and International Celestial Reference System (ICRS) groups.

So as the jet recedes from the runner, the jet velocity relative to the runner is: −(Vi − u) = −Vi \+ u. In the standard reference frame (relative to the earth), the final velocity is then: Vf = (−Vi \+ u) \+ u = −Vi \+ 2u.

The Catalogue of Fundamental Stars is a series of six astrometric catalogues of high precision positional data for a small selection of stars to define a celestial reference frame, which is a standard coordinate system for measuring positions of stars.

An object's orbital parameters will be different if they are expressed with respect to a non-inertial reference frame (for example, a frame co-precessing with the primary's equator), than if it is expressed with respect to a (non-rotating) inertial reference frame. Put in more general terms, a perturbed trajectory can be analysed as if assembled of points, each of which is contributed by a curve out of a sequence of curves. Variables parameterising the curves within this family can be called orbital elements. Typically (though not necessarily), these curves are chosen as Keplerian conics, all of which share one focus.

The invariance properties of molecular descriptors can be defined as the ability of the algorithm for their calculation to give a descriptor value that is independent of the particular characteristics of the molecular representation, such as atom numbering or labeling, spatial reference frame, molecular conformations, etc. Invariance to molecular numbering or labeling is assumed as a minimal basic requirement for any descriptor. Two other important invariance properties, translational invariance and rotational invariance, are the invariance of a descriptor value to any translation or rotation of the molecules in the chosen reference frame. These last invariance properties are required for the 3D-descriptors.

Two bodies falling towards the center of the Earth accelerate towards each other as they fall. The equivalence between gravitational and inertial effects does not constitute a complete theory of gravity. When it comes to explaining gravity near our own location on the Earth's surface, noting that our reference frame is not in free fall, so that fictitious forces are to be expected, provides a suitable explanation. But a freely falling reference frame on one side of the Earth cannot explain why the people on the opposite side of the Earth experience a gravitational pull in the opposite direction.

72 (1967), p.1324-6. albeit that the time unit of TDB, if measured by the hypothetical observer described above, at rest in the reference frame and at infinite distance, would be very slightly slower than the SI second (by 1 part in 1/LB = 1 part in 108/1.550519768).Scaling defined in IAU 2006 resolution 3. Geocentric Coordinate Time (TCG) is based on a reference frame comoving with the geocenter (the center of the Earth), and is defined in principle for use for calculations concerning phenomena on or in the region of the Earth, such as planetary rotation and satellite motions.

The standard defines the requirements of an hierarchical DGG, including how to operate the grid. Any DGG that satisfies these requirements can be named DGGS. "A DGGS specification SHALL include a DGGS Reference Frame and the associated Functional Algorithms as defined by the DGGS Core Conceptual Data Model".Section 6.1, "DGGS Core Data Model Overview", of the DGGS standard : For an Earth grid system to be compliant with this Abstract Specification it must define a hierarchical tessellation of equal area cells that both partition the entire Earth at multiple levels of granularity and provide a global spatial reference frame.

The equivalence principle can be understood by comparing a rocket ship in two scenarios. First, imagine a rocket ship that is at rest on the Earth's surface; objects dropped within the rocket ship will fall towards the floor with an acceleration of . Now, imagine a distant rocket ship that has escaped Earth's gravitational field and is accelerating at a constant due to thrust from its rockets; objects in the rocket ship that are unconstrained will move towards the floor with an acceleration of . This example shows one way that a uniformly accelerating reference frame is indistinguishable from a gravitational reference frame.

Consider a simple physics problem: a car is moving such that it covers a distance of 1 mile in every 2 minutes, what is its velocity in metres per second? With some conversion and calculation, one can come up with the answer "13.41m/s"; on the other hand, one can instead answer "0, relative to itself". The first answer is correct because it recognises a reference frame is implied in the problem. The second one, albeit pedantic, is also correct because it exploits the fact that there is not a particular reference frame specified by the problem.

Some authors interpret the first law as defining what an inertial reference frame is; from this point of view, the second law holds only when the observation is made from an inertial reference frame, and therefore the first law cannot be proved as a special case of the second. Other authors do treat the first law as a corollary of the second. The explicit concept of an inertial frame of reference was not developed until long after Newton's death. In the given interpretation mass, acceleration, momentum, and (most importantly) force are assumed to be externally defined quantities.

Fictitious forces can be considered to do work, provided that they move an object on a trajectory that changes its energy from potential to kinetic. For example, consider a person in a rotating chair holding a weight in their outstretched hand. If they pull their hand inward toward their body, from the perspective of the rotating reference frame, they have done work against the centrifugal force. When the weight is let go, it spontaneously flies outward relative to the rotating reference frame, because the centrifugal force does work on the object, converting its potential energy into kinetic.

A smaller body (either artificial or natural) may gain heliocentric velocity due to gravity assist – this effect can change the body's mechanical energy in heliocentric reference frame (although it will not changed in the planetary one). However, such selection of "geocentric" or "heliocentric" frames is merely a matter of computation. It does not have philosophical implications and does not constitute a distinct physical or scientific model. From the point of view of general relativity, inertial reference frames do not exist at all, and any practical reference frame is only an approximation to the actual space-time, which can have higher or lower precision.

In fluid dynamics and plasma physics, the Clebsch representation provides a means to overcome the difficulties to describe an inviscid flow with non-zero vorticity – in the Eulerian reference frame – using Lagrangian mechanics and Hamiltonian mechanics. At the critical point of such functionals the result is the Euler equations, a set of equations describing the fluid flow. Note that the mentioned difficulties do not arise when describing the flow through a variational principle in the Lagrangian reference frame. In case of surface gravity waves, the Clebsch representation leads to a rotational-flow form of Luke's variational principle.

Which type of spatial knowledge is acquired in a special situation depends also from the respective source of information. Active navigation appears to have a bigger impact on the establishment of route knowledge, whereas the use of a map seemingly better supports survey knowledge about more large-scaled complex environments. In this context, a discussion came up about different reference frames, which are the frameworks wherein spatial information is encoded. In general, two of them can be distinguished as the egocentric (Latin ego: “I”) and the allocentric (ancient Greek allos: “another, external”) reference frame. Within an egocentric reference frame, spatial information is encoded in terms of relations to the physical body of a navigator, whereas the allocentric reference frame defines relations of objects among each other, that is independent of the physical body of an “observer” and thus in a more absolute way, which takes metrical conditions and general alignments like cardinal directions into account.

When moving within a rotating reference frame such as in a centrifuge or environment where gravity is simulated with centrifugal force, the coriolis effect causes a sense of motion in the vestibular system that does not match the motion that is seen.

W. J. Morgan and J. P. Morgan. Plate velocities in hotspot reference frame: electronic supplement. The seamount is about 7 million years old. It incorporates a tropical to subtropical, very shallow water calcareous algal/encrusting foraminiferid biota, suggesting deposition in water deep.

In 1987 the bureau's tasks of combining different measurements of Universal Time were taken over by the BIPM. Its tasks related to the correction of time with respect to the celestial reference frame and the earth's rotation were taken over by the IERS.

Mach effects are relativistic by nature, and considering a spaceship accelerating with a Mach effect thruster, the propellant is not accelerating with the ship, so the situation should be treated as an accelerating and therefore non-inertial reference frame, where F does not equal ma.

Einstein's theory of special relativity mostly (though not universally) made theories of time where there is something metaphysically special about the present seem much less plausible, as the reference-frame-dependence of time seems to not allow the idea of a privileged present moment.

Like its neighbour, the Tasmantid Seamount Chain has resulted from the Indo-Australian Plate moving northward over a stationary hotspot.W. J. Morgan and J. P. Morgan. Plate velocities in hotspot reference frame: electronic supplement. It ranges in age from 40 to 6 million years old.

In the context of special relativity, it is natural to join the magnetic vector potential together with the (scalar) electric potential into the electromagnetic potential, also called four-potential. One motivation for doing so is that the four-potential is a mathematical four-vector. Thus, using standard four-vector transformation rules, if the electric and magnetic potentials are known in one inertial reference frame, they can be simply calculated in any other inertial reference frame. Another, related motivation is that the content of classical electromagnetism can be written in a concise and convenient form using the electromagnetic four potential, especially when the Lorenz gauge is used.

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.

Thus a ruler that is one metre long in one frame of reference will not be one metre long in a reference frame that is moving relative to the first frame. This means the length of an object varies depending on the speed of the observer.

In physics the Einstein aether theory, also called aetheory, is a generally covariant modification of general relativity which describes a spacetime endowed with both a metric and a unit timelike vector field named the aether. The theory has a preferred reference frame and hence violates Lorentz invariance.

The United States Naval Observatory Flagstaff Station (NOFS), is an astronomical observatory near Flagstaff, Arizona, USA. It is the national dark-sky observing facility under the United States Naval Observatory (USNO). NOFS and USNO combine as the Celestial Reference Frame manager for the U.S. Secretary of Defense.

W. J. Morgan and J. P. Morgan. Plate velocities in hotspot reference frame: electronic supplement. On the Australian mainland, a third north-south sequence of extinct volcanoes (which includes the Glass House Mountains) is likely to have the same origin. The chain formed during the Miocene.

Nostell, a smaller village to the west and is currently grouped with Hessle and Hill Top as well as several other small parishes as a division of Wakefield city council, and Pontefract, another large town to the north and a common reference frame for where the parish is located.

Nowadays, UT is the observed orientation of the Earth relative to an inertial reference frame formed by extra-galactic radio sources, modified by an adopted ratio between sidereal time and solar time. Its measurement by several observatories is coordinated by the International Earth Rotation and Reference Systems Service (IERS).

A fictitious force (also called a pseudo force, d'Alembert force, or inertial forceNASA notes:(23) Accelerated Frames of Reference: Inertial Forces) is a force that appears to act on a mass whose motion is described using a non- inertial frame of reference, such as an accelerating or rotating reference frame. An example is seen in a passenger vehicle that is accelerating in the forward direction - passengers perceive that they are acted upon by a force in the rearward direction pushing them back into their seats. An example in a rotating reference frame is the force that appears to push objects outwards towards the rim of a centrifuge. These apparent forces are examples of fictitious forces.

ET's direct successor for measuring time on a geocentric basis was Terrestrial Dynamical Time (TDT). The new time scale to supersede ET for planetary ephemerides was to be Barycentric Dynamical Time (TDB). TDB was to tick uniformly in a reference frame comoving with the barycenter of the Solar System. (As with any coordinate time, a corresponding clock, to coincide in rate, would need not only to be at rest in that reference frame, but also (an unattainable hypothetical condition) to be located outside all of the relevant gravity wells.) In addition, TDB was to have (as observed/evaluated at the Earth's surface), over the long term average, the same rate as TDT (now TT).

An inertial frame of reference in classical physics and special relativity possesses the property that in this frame of reference a body with zero net force acting upon it does not accelerate; that is, such a body is at rest or moving at a constant velocity. An inertial frame of reference can be defined in analytical terms as a frame of reference that describes time and space homogeneously, isotropically, and in a time-independent manner. Conceptually, the physics of a system in an inertial frame have no causes external to the system. An inertial frame of reference may also be called an inertial reference frame, inertial frame, Galilean reference frame, or inertial space.

Etalon-1 and Etalon-2 are two geodetic satellites designed to determine with high accuracy terrestrial reference frame and earth rotation parameters, to improve the gravity field, and to improve the gravitational constant. Each satellite is a high-density passive laser reflector in a very stable medium Earth orbit (MEO).

The following is similar to that of Einstein. As in the Galilean transformation, the Lorentz transformation is linear since the relative velocity of the reference frames is constant as a vector; otherwise, inertial forces would appear. They are called inertial or Galilean reference frames. According to relativity no Galilean reference frame is privileged.

The system must also include encoding methods to: address each cell; assign quantized data to cells; and perform algebraic operations on the cells and the data assigned to them. Main concepts of the DGGS Core Conceptual Data Model: # reference frame elements, and, # functional algorithm elements; comprising: ## quantization operations, ## algebraic operations, and ## interoperability operations.

The Milky Way Galaxy is moving through space and many astronomers believe the velocity of this motion to be approximately relative to the observed locations of other nearby galaxies. Another reference frame is provided by the Cosmic microwave background. This frame of reference indicates that the Milky Way is moving at around .

Relativistic time dilation refers to the fact that a clock (indicating its proper time in its rest frame) that moves relative to an observer is observed to run slower. The situation is depicted in symmetric Loedel diagrams to the right. Note that we can compare spacetime lengths on page directly with each other, due to the symmetric nature of the Loedel diagram. The observer whose reference frame is given by the black axes is assumed to move from the origin O towards A. The moving clock has the reference frame given by the blue axes and moves from O to B. For the black observer, all events happening simultaneously with the event at A are located on a straight line parallel to its space axis.

Observers inside a closed box that is moving with a constant velocity cannot detect their own motion; however, observers within an accelerating reference frame can detect that they are in a non-inertial reference frame from the fictitious forces that arise. For example, for straight-line acceleration Vladimir Arnold presents the following theorem: Other accelerations also give rise to fictitious forces, as described mathematically below. The physical explanation of motions in an inertial frame is the simplest possible, requiring no fictitious forces: fictitious forces are zero, providing a means to distinguish inertial frames from others.As part of the requirement of simplicity, to be an inertial frame, in all other frames that differ only by a uniform rate of translation, the description should be of the same form.

In light-front coordinates, x^+=ct+z, x^-=ct-z, the spatial coordinates x,y,z do not enter symmetrically: the coordinate z is distinguished, whereas x and y do not appear at all. This non-covariant definition destroys the spatial symmetry that, in its turn, results in a few difficulties related to the fact that some transformation of the reference frame may change the orientation of the light-front plane. That is, the transformations of the reference frame and variation of orientation of the light-front plane are not decoupled from each other. Since the wave function depends dynamically on the orientation of the plane where it is defined, under these transformations the light-front wave function is transformed by dynamical operators (depending on the interaction).

When a car moves over the ground the boundary layer on the ground becomes helpful. In the reference frame of the car, the ground is moving backwards at some speed. As the ground moves, it pulls on the air above it and causes it to move faster. This enhances the Bernoulli effect and increases downforce.

This is an example of an inertial effect that causes light to bend. The equivalence principle states that this inertial phenomenon will occur in a gravitational reference frame as well. Indeed, the phenomenon of gravitational lensing states that matter can bend light, and this phenomenon has been observed by the Hubble Telescope, and other experiments.

Block motion compensation (BMC), also known as motion-compensated discrete cosine transform (MC DCT), is the most widely used motion compensation technique. In BMC, the frames are partitioned in blocks of pixels (e.g. macro-blocks of 16×16 pixels in MPEG). Each block is predicted from a block of equal size in the reference frame.

It was superseded by the quasar-based International Celestial Reference Frame (ICRF). The Fifth Fundamental Catalogue Extension (FK5), published in 1991, added 3,117 new stars. The Sixth Fundamental Catalogue (FK6) is a 2000 update of FK5 correlated with the ICRF through the Hipparcos satellite. It comes in two parts: FK6(I) and FK6(III).

Thus, momentum is conserved in both reference frames. Moreover, as long as the force has the same form, in both frames, Newton's second law is unchanged. Forces such as Newtonian gravity, which depend only on the scalar distance between objects, satisfy this criterion. This independence of reference frame is called Newtonian relativity or Galilean invariance.

At the von Neumann spike point the explosive still remains unreacted. The spike marks the onset of the zone of exothermic chemical reaction, which finishes at the Chapman-Jouguet state. After that, the detonation products expand backward. In the reference frame in which the shock is stationary, the flow following the shock is subsonic.

By monitoring the amplitude of received microseisms from the same source using seismographs, information on the source amplitude can be derived. Because the solid earth provides a fixed reference frame, the transit time of the microseisms from the source is constant, and this provides a control for the variable transit time of the microbaroms through the moving atmosphere.

As seen in a rotating reference frame that matches the angular velocity of the two co- orbiting bodies, the gravitational fields of two massive bodies combined providing the centripetal force at the Lagrangian points, allowing the smaller third body to be relatively stationary with respect to the first two."Lagrange Points" by Enrique Zeleny, Wolfram Demonstrations Project.

A global hotspot reference frame has been postulated (see, e.g., W. Jason Morgan) but there is now evidence that not all hotspots are necessarily fixed in their locations relative to one another or the earth's spin axis. However, there are groups of such hotspots that appear to be fixed within the constraints of available data, within particular mesoplates.

For the times postdating the assembly of Pangea (320 Ma), synthetic APWPs are often constructed in the reference frame fixed to the African plate because Africa has occupied a central position in the Pangea configuration and has been dominantly surrounded by spreading ridges after the Pangea breakup, which commenced in the early Jurassic (ca. 180 Ma).

Michael Krausz, Limits of Rightness, chap. 13. II. Relativism. In addition, Krausz’s work on relativism canvasses the range and significance of relativistic doctrines and rehearses their virtues and vices. He considers relativism as the claim that truth, goodness, or beauty (among other values) is relative to some reference frame, and no absolute standards to adjudicate between reference frames exist.

A right spherical hypercone can be described by the function : \vec \sigma (\phi, \theta, t) = (t s \cos \theta \cos \phi, t s \cos \theta \sin \phi, t s \sin \theta, t) with vertex at the origin and expansion speed s. An oblique spherical hypercone could then be described by the function : \vec \sigma (\phi, \theta, t) = (v_x t + t s \cos \theta \cos \phi, v_y t + t s \cos \theta \sin \phi, v_z t + t s \sin \theta, t) where (v_x, v_y, v_z) is the 3-velocity of the center of the expanding sphere. An example of such a cone would be an expanding sound wave as seen from the point of view of a moving reference frame: e.g. the sound wave of a jet aircraft as seen from the jet's own reference frame.

It performs key quasar-based reference frame operations, transit detections of exoplanets, Vilnius photometry, M-Dwarf star analysis, dynamical system analysis, reference support to orbiting space object information, horizontal parallax guide support to NPOI, and it performs photometric operations support to astrometric studies (along with its newer siblings). The 40-inch telescope can carry a number of liquid nitrogen-cooled cameras, a coronagraph, and a nine-stellar magnitude neutral density spot focal plane array camera, through which star positions are cross-checked before use in fundamental NPOI reference frame astrometry. This telescope is also used to test internally developed optical adaptive optics (AO) systems, using tip-tilt and deformable mirror optics. The Shack–Hartmann AO system allows for corrections of the wavefront's aberrations caused by scintillation (degraded seeing), to higher Zernike polynomials.

1977, DE111 in May 1980, DE118 in Sep. 1981, and DE200 in 1982. DE102 was the first numerically integrated so-called Long Ephemeris, covering much of history for which useful astronomical observations were available: 1141 BC to AD 3001. DE200, a version of DE118 migrated to the J2000.0 reference frame, was adopted as the fundamental ephemeris for the new almanacs starting in 1984.

However, an inertial frame can always be found which is momentarily comoving with the particle. This frame, the momentarily comoving reference frame (MCRF), enables application of special relativity to the analysis of accelerated particles. If an inertial observer looks at an accelerating clock, only the clock's instantaneous speed is important when computing time dilation. The converse, however, is not true.

Since the stars are light years away, this observation means that, in the non-inertial reference frame of the Earth, anybody who looks at the stars is seeing objects which appear, to them, to be moving faster than the speed of light. Since non-inertial reference frames do not abide by the special principle of relativity, such situations are not self-contradictory.

In mathematics, a Lagrangian system is a pair , consisting of a smooth fiber bundle and a Lagrangian density , which yields the Euler–Lagrange differential operator acting on sections of . In classical mechanics, many dynamical systems are Lagrangian systems. The configuration space of such a Lagrangian system is a fiber bundle over the time axis . In particular, if a reference frame is fixed.

72 (1967), p.1324-6. and overall will remain at less than 2 milliseconds for several millennia.IAU 2006 resolution 3, see Recommendation and footnotes, note 3. TDB applies to the Solar-System-barycentric reference frame, and was first defined in 1976 as a successor to the (non-relativistic) former standard of ephemeris time (adopted by the IAU in 1952 and superseded 1976).

In physics, general covariant transformations are symmetries of gravitation theory on a world manifold X. They are gauge transformations whose parameter functions are vector fields on X. From the physical viewpoint, general covariant transformations are treated as particular (holonomic) reference frame transformations in general relativity. In mathematics, general covariant transformations are defined as particular automorphisms of so-called natural fiber bundles.

Although general relativity implies that there are no true inertial frames around gravitating bodies, the ICRF is important because it does not exhibit any measurable angular motion since the extragalactic sources used to define the ICRF are so far away. The ICRF is now the standard reference frame used to define the positions of the planets (including the Earth) and other astronomical objects.

Reference frames are frames of a compressed video that are used to define future frames. As such, they are only used in inter-frame compression techniques. In older video encoding standards, such as MPEG-2, only one reference frame – the previous frame – was used for P-frames. Two reference frames (one past and one future) were used for B-frames.

According to Einstein's special theory of relativity, it is impossible to say in an absolute sense that two distinct events occur at the same time if those events are separated in space. If one reference frame assigns precisely the same time to two events that are at different points in space, a reference frame that is moving relative to the first will generally assign different times to the two events (the only exception being when motion is exactly perpendicular to the line connecting the locations of both events). For example, a car crash in London and another in New York appearing to happen at the same time to an observer on Earth, will appear to have occurred at slightly different times to an observer on an airplane flying between London and New York. Furthermore, if the two events cannot be causally connected (i.e.

Vertical arrangement as suggested by Bell. In Bell's version of the thought experiment, three spaceships A, B and C are initially at rest in a common inertial reference frame, B and C being equidistant to A. Then, a signal is sent from A to reach B and C simultaneously, causing B and C starting to accelerate in the vertical direction (having been pre-programmed with identical acceleration profiles), while A stays at rest in its original reference frame. According to Bell, this implies that B and C (as seen in A's rest frame) "will have at every moment the same velocity, and so remain displaced one from the other by a fixed distance." Now, if a fragile thread is tied between B and C, it's not long enough anymore due to length contractions, thus it will break.

An accelerometer at rest relative to the Earth's surface will indicate approximately 1 g upwards because the Earth's surface exerts a normal force upwards relative to the local inertial frame (the frame of a freely falling object near the surface). To obtain the acceleration due to motion with respect to the Earth, this "gravity offset" must be subtracted and corrections made for effects caused by the Earth's rotation relative to the inertial frame. The reason for the appearance of a gravitational offset is Einstein's equivalence principle, which states that the effects of gravity on an object are indistinguishable from acceleration. When held fixed in a gravitational field by, for example, applying a ground reaction force or an equivalent upward thrust, the reference frame for an accelerometer (its own casing) accelerates upwards with respect to a free-falling reference frame.

Nations that touch the Equator (red) and the Prime Meridian (blue) The IERS Reference Meridian (IRM), also called the International Reference Meridian, is the prime meridian (0° longitude) maintained by the International Earth Rotation and Reference Systems Service (IERS). It passes about 5.3 arcseconds east of George Biddell Airy's 1851 transit circle or at the latitude of the Royal Observatory, Greenwich.IRM on grounds of Royal Observatory from Google Earth Accessed 30 March 2012The astronomic latitude of the Royal Observatory is 51°28'38"N whereas its latitude on the European Terrestrial Reference Frame (1989) datum is 51°28'40.1247"N. It is also the reference meridian of the Global Positioning System (GPS) operated by the United States Department of Defense, and of WGS84 and its two formal versions, the ideal International Terrestrial Reference System (ITRS) and its realization, the International Terrestrial Reference Frame (ITRF).

An even field has pixel information for lines 2, 4, 6...1080. When video is sent in interlaced-scan format, each frame is sent in two fields, the field of odd-numbered lines followed by the field of even-numbered lines. A frame used as a reference for predicting other frames is called a reference frame. Frames encoded without information from other frames are called I-frames.

The stellar aberration is purely an effect of the change of the reference frame. The astronomer orbits (with Earth) around the Sun and furthermore rotates around the axis of Earth. His current rest frame S' therefore has different velocities relative to the rest frame S of the barycenter of the Solar System at different times. Hence the astronomer observes that the position of the star changes.

Also with the introduction of the International Celestial Reference Frame, all objects near and far are put fundamentally in relationship to a large frame based on very distant fixed radio sources, and the choice of the origin is arbitrary and defined for the convenience of the problem at hand. There are no significant problems in astronomy where the ecliptic and the equinox need to be defined.

On spaceships, map-clocks may look unsynchronized. Event B is simultaneous with A in the green reference frame, but it occurred before in the blue frame, and will occur later in the red frame. Events A, B, and C occur in different order depending on the motion of the observer. The white line represents a plane of simultaneity being moved from the past to the future.

Motl writes a science and politics blog called "The Reference Frame: Supersymmetric world from a conservative viewpoint", which has been described as an "over-the-top" defense of string theory. Following the example of Oriana Fallaci, he characterizes himself as a Christian atheist. Motl also describes himself as a "champion of the Consistent Histories interpretation of quantum mechanics", and has strongly criticised Erik Verlinde's entropic gravity theory.

Minkowski diagram for 3 coordinate systems. For the speeds relative to the system in black and holds. Another postulate of special relativity is the constancy of the speed of light. It says that any observer in an inertial reference frame measuring the vacuum speed of light relative to themself obtains the same value regardless of his own motion and that of the light source.

Special relativity revised the transformation of forces in moving reference frames to be consistent with Lorentz invariance. The details of these transformations are discussed below. In addition to consistency, it would be nice to consolidate the descriptions so they appear to be frame-independent. A clue to a framework-independent description is the observation that magnetic fields in one reference frame become electric fields in another frame.

History of the Prime Meridian -Past and PresentIRM on grounds of Royal Observatory from Google Earth Accessed 30 March 2012The astronomic latitude of the Royal Observatory is 51°28'38"N whereas its latitude on the European Terrestrial Reference Frame (1989) datum is 51°28'40.1247"N. A current convention on the Earth uses the opposite of the IRM as the basis for the International Date Line.

There is a special meaning of the expression "equinox (and ecliptic/equator) of date". When coordinates are expressed as polynomials in time relative to a reference frame defined in this way, that means the values obtained for the coordinates in respect of any interval t after the stated epoch, are in terms of the coordinate system of the same date as the obtained values themselves, i.e.

Stellar drift, or the motion of stars, is a necessary result of the lack of an absolute reference frame in special relativity. Nothing in space stands still—more precisely, standing still is meaningless without defining what "still" means. Most galaxies have been moving away ever since the Big Bang, as explained by the metric expansion of space. Galaxy motion is also influenced by galaxy groups and clusters.

This algorithm calculates the cost function at each possible location in the search window. This leads to the best possible match of the macro-block in the reference frame with a block in another frame. The resulting motion compensated image has highest peak signal-to-noise ratio as compared to any other block matching algorithm. However this is the most computationally extensive block matching algorithm among all.

A basis (or reference frame) of a (universal) algebra is a function b that takes some algebra elements as values b(i) and satisfies either one of the following two equivalent conditions. Here, the set of all b(i) is called the basis set, whereas several authors call it the "basis".Gould.Grätzer 1968, p.198. The set I of its arguments i is called the dimension set.

The use of the inertia matrix in Newton's second law assumes its components are computed relative to axes parallel to the inertial frame and not relative to a body-fixed reference frame. This means that as the body moves the components of the inertia matrix change with time. In contrast, the components of the inertia matrix measured in a body-fixed frame are constant.

These are then referred to by one or more 'datum references' which indicate measurements that should be made with respect to the corresponding datum feature . In geometric dimensioning and tolerancing, datum reference frames are typically 3D. Datum reference frames are used as part of the feature control frame to show where the measurement is taken from. A typical datum reference frame is made up of three planes.

The Lagrangian approach follows a fluid mass of fixed identity as it moves through a flowfield. The Eulerian reference frame, in contrast, does not move with the fluid. Rather it is a fixed frame or control volume that fluid flows through. The Eulerian frame is most useful in a majority of compressible flow problems, but requires that the equations of motion be written in a compatible format.

Practical navigation systems are in general referenced to a specific ITRF solution, or to their own coordinate systems which are then referenced to an ITRF solution. The ITRS and ITRF solutions are maintained by the International Earth Rotation and Reference Systems Service (IERS). For example, the Galileo Terrestrial Reference Frame (GTRF) is used for the Galileo navigation system; currently defined as ITRF2005 by the European Space Agency.

After restoring the middle of the Skagerrak-Centered Large Igneous Province (SCLIP) using a new reference frame, it has been shown that the Skagerrak plume rose from the core–mantle boundary (CMB) to its ~300 Ma position. The major eruption interval took place in very narrow time interval, of 297 Ma ± 4 Ma. The rift formation coincides with the Moskovian/Kasimovian boundary and the Carboniferous Rainforest Collapse.

Stellar rotation is measured through Doppler shift or by tracking active surface features. This rotation induces a centrifugal acceleration in the reference frame of the Earth which slightly counteracts the effect of gravity the closer one is to the equator. One effect is that an object weighs slightly less at the equator. Another is that the Earth is slightly deformed into an oblate spheroid.

The coordinate times cannot be measured, but only computed from the (proper-time) readings of real clocks with the aid of the time dilation relationship shown in equation () (or some alternative or refined form of it). Only for explanatory purposes it is possible to conceive a hypothetical observer and trajectory on which the proper time of the clock would coincide with coordinate time: such an observer and clock have to be conceived at rest with respect to the chosen reference frame (v = 0 in () above) but also (in an unattainably hypothetical situation) infinitely far away from its gravitational masses (also U = 0 in () above).S A Klioner (2008), cited above, at page 955. Even such an illustration is of limited use because the coordinate time is defined everywhere in the reference frame, while the hypothetical observer and clock chosen to illustrate it has only a limited choice of trajectory.

For the philosopher Edward W. James, astrology is irrational not because of the numerous problems with mechanisms and falsification due to experiments, but because an analysis of the astrological literature shows that it is infused with fallacious logic and poor reasoning. This poor reasoning includes appeals to ancient astrologers such as Kepler despite any relevance of topic or specific reasoning, and vague claims. The claim that evidence for astrology is that people born at roughly "the same place have a life pattern that is very similar" is vague, but also ignores that time is reference frame dependent and gives no definition of "same place" despite the planet's moving in the reference frame of the solar system. Other comments by astrologers are based on severely erroneous interpretations of basic physics, such as a claim by one astrologer that the solar system looks like an atom.

Almost all science- fiction stories which use this concept actively, such as to enable time travel, oversimplify this concept to a one-dimensional timeline to fit a linear structure, which does not fit models of reality. Such time machines are often portrayed as being instantaneous, with its contents departing one time and arriving in another—but at the same literal geographic point in space. This is often carried out without note of a reference frame, or with the implicit assumption that the reference frame is local; as such, this would require either accurate teleportation, as a rotating planet, being under acceleration, is not an inertial frame, or for the time machine to remain in the same place, its contents 'frozen'. Author Oliver Franklin published a science fiction work in 2008 entitled World Lines in which he related a simplified explanation of the hypothesis for laymen.

Thus, it is very common for computational optimizing programs to flip back and forth between representations during their iterations. This can dominate the calculation time of the potential itself and in long chain molecules introduce cumulative numerical inaccuracy. While all conversion algorithms produce mathematically identical results, they differ in speed and numerical accuracy. Currently, the fastest and most accurate torsion to Cartesian conversion is the Natural Extension Reference Frame (NERF) method.

Robot arms, Stewart platforms, and humanoid robotic systems are also examples of spatial mechanisms. Bennett's linkage is an example of a spatial overconstrained mechanism, which is constructed from four hinged joints. The group SE(3) is six-dimensional, which means the position of a body in space is defined by six parameters. Three of the parameters define the origin of the moving reference frame relative to the fixed frame.

It is listed as a sednoid by some. However, is usually considered to be an extreme trans-Neptunian object and not a sednoid, due to its high eccentricity which makes the heliocentric orbit unstable. In the heliocentric reference frame, the perihelion is currently rising, and the nominal orbit has a perihelion distance above only since October 2018. is estimated to be about in diameter and moderately red in color.

Einstein based his theory of special relativity on two fundamental postulates. First, all physical laws are the same for all inertial frames of reference, regardless of their relative state of motion; and second, the speed of light in free space is the same in all inertial frames of reference, again, regardless of the relative velocity of each reference frame. The Lorentz transformation is fundamentally a direct consequence of this second postulate.

53 (1992), pp. 81-109. Two events are called simultaneous in a chosen reference frame if and only if the chosen coordinate time has the same value for both of them;S A Klioner (2008), "Relativistic scaling of astronomical quantities and the system of astronomical units", Astronomy and Astrophysics, vol.478 (2008), pp.951-958, at section 5: "On the concept of coordinate time scales", esp. p.955.

From 1956 until 1987 the International Time Bureau was part of the Federation of Astronomical and Geophysical Data Analysis Services (FAGS). In 1987 the bureau's tasks of combining different measurements of Atomic Time were taken over by the BIPM. Its tasks related to the correction of time with respect to the celestial reference frame and the earth's rotation in order to realize UTC were taken over by the IERS.

This description of the orientation of the reference frame is somewhat simplified; the orientation is not quite fixed. A slow motion of Earth's axis, precession, causes a slow, continuous turning of the coordinate system westward about the poles of the ecliptic, completing one circuit in about 26,000 years. Superimposed on this is a smaller motion of the ecliptic, and a small oscillation of the Earth's axis, nutation.Explanatory Supplement (1961), pp.

Some systems in fluid dynamics involve a fluid being subject to conservative body forces. Since a conservative body force is the gradient of some potential function, it has the same effect as a gradient in fluid pressure. It is often convenient to define a modified pressure equal to the true fluid pressure plus the potential. Examples of conservative body forces include gravity and the centrifugal force in a rotating reference frame.

"P-frame" is an abbreviation for "Predicted-frame". They may also be called forward-predicted frames or inter-frames (B-frames are also inter-frames). P-frames exist to improve compression by exploiting the temporal (over time) redundancy in a video. P-frames store only the difference in image from the frame (either an I-frame or P-frame) immediately preceding it (this reference frame is also called the anchor frame).

The reference frame in the target image is stationary, while the other datasets are transformed to match to the target. Intensity-based methods compare intensity patterns in images via correlation metrics, while feature- based methods find correspondence between image features such as points, lines, and contours. Intensity-based methods register entire images or sub- images. If sub-images are registered, centers of corresponding sub images are treated as corresponding feature points.

Example encounter. In the planet's frame of reference, the space probe leaves with the exact same speed at which it had arrived. But when observed in the reference frame of the Solar System (fixed to the Sun), the benefit of this maneuver becomes apparent. Here it can be seen how the probe gains speed by tapping energy from the speed of the planet as it orbits the Sun.

Unlike former astronomical time scales, TCB is defined in the context of the general theory of relativity. The relationships between TCB and other relativistic time scales are defined with fully general relativistic metrics. Because the reference frame for TCB is not influenced by the gravitational potential caused by the Solar system, TCB ticks faster than clocks on the surface of the Earth by 1.550505 × 10−8 (about 490 milliseconds per year).

Sketch of a circumlunar free return trajectory (not to scale), plotted on the rotating reference frame rotating with the moon. A free-return trajectory is a trajectory of a spacecraft traveling away from a primary body (for example, the Earth) where gravity due to a secondary body (for example, the Moon) causes the spacecraft to return to the primary body without propulsion (hence the term free).Diagram of the free return .

Also equations of motion can be formulated which connect acceleration and force. Equations for several forms of acceleration of bodies and their curved world lines follow from these formulas by integration. Well known special cases are hyperbolic motion for constant longitudinal proper acceleration or uniform circular motion. Eventually, it is also possible to describe these phenomena in accelerated frames in the context of special relativity, see Proper reference frame (flat spacetime).

A geosynchronous orbit can have any inclination. Satellites commonly have an inclination of zero, ensuring that the orbit remains over the equator at all times, making it stationary with respect to latitude from the point of view of a ground observer (and in the ECEF reference frame). Another popular inclinations is 63.4° for a Tundra orbit, which ensures that the orbit's argument of perigee doesn't change over time.

By the 1880s, there was a prominent paradox that an observer within Maxwell's electromagnetic field measured it at approximately constant speed, regardless of the observer's speed relative to other objects within the electromagnetic field. Thus, although the observer's speed was continually lost relative to the electromagnetic field, it was preserved relative to other objects in the electromagnetic field. And yet no violation of Galilean invariance within physical interactions among objects was detected. As Maxwell's electromagnetic field was modeled as oscillations of the aether, physicists inferred that motion within the aether resulted in aether drift, shifting the electromagnetic field, explaining the observer's missing speed relative to it. The Galilean transformation had been the mathematical process used to translate the positions in one reference frame to predictions of positions in another reference frame, all plotted on Cartesian coordinates, but this process was replaced by Lorentz transformation, modeled by the Dutch Hendrik Lorentz [1853–1928].

The fictitious force F is due to an object's inertia when the reference frame does not move inertially, and thus begins to accelerate relative to the free object. The fictitious force thus does not arise from any physical interaction between two objects, such as electromagnetism or contact forces, but rather from the acceleration a of the non-inertial reference frame itself, which from the viewpoint of the frame now appears to be an acceleration of the object instead, requiring a "force" to make this happen. As stated by Iro:In this connection, it may be noted that a change in coordinate system, for example, from Cartesian to polar, if implemented without any change in relative motion, does not cause the appearance of fictitious forces, despite the fact that the form of the laws of motion varies from one type of curvilinear coordinate system to another. Assuming Newton's second law in the form F = ma, fictitious forces are always proportional to the mass m.

A simple example of an object with moving parts but zero total momentum is a container of gas. In this case, the mass of the container is given by its total energy (including the kinetic energy of the gas molecules), since the system's total energy and invariant mass are the same in any reference frame where the momentum is zero, and such a reference frame is also the only frame in which the object can be weighed. In a similar way, the theory of special relativity posits that the thermal energy in all objects (including solids) contributes to their total masses and weights, even though this energy is present as the kinetic and potential energies of the atoms in the object, and it (in a similar way to the gas) is not seen in the rest masses of the atoms that make up the object. Similarly, even photons, if trapped in an isolated container, would contribute their energy to the mass of the container.

Two approaches can be used (often in combination) to elucidate how a particular lake works: field measurements and mathematical modeling. One common technique for field measurement is to introduce a tracer into the lake and monitor its movement. This can be a solid tracer, such as a float constructed to be neutrally buoyant within a particular water layer, or sometimes a liquid. This approach is sometimes referred to as using a Lagrangian reference frame.

A reference frame is a way someone can represent their location in space, and evidence has shown that our spatial experience involves the combination of our sensory inputs from two specific reference frames including egocentric and allocentric.Galati, G., Lobel, E., Vallar, G., Berthoz, A., Pizzamiglio, L., & Le Bihan D. (2000) The neural basis of egocentric and allocentric coding of space in humans: a functional magnetic resonance study. Exp Brain Res. 133, 2, 156-64.

Smith has also taken a stance towards a relativistic rehabilitation of geocentrism. He does not support a Ptolemaic or medieval geocentrism unequivocally, nor assert that heliocentrism is absolutely false. Rather, he argues that, according to the theory of relativity, both heliocentrism and geocentrism have scientific merit, insofar as scientific observation depends upon the reference frame of the observer. Consequently, any observations made from Earth (or any near- Earth satellites) are in effect geocentric..

VP8 only supports progressive scan video signals with 4:2:0 chroma subsampling and 8 bits per sample. In its first public version, On2's VP8 implementation supports multi-core processors with up to 64 cores simultaneously. At least in the implementation (from August 2011), VP8 is comparatively badly adapted to high resolutions (HD). With only three reference frame buffers needed, VP8 enables for decoder implementations with a relatively small memory footprint.

Relative sea level (abbreviated as RSL) is defined as the sea level that is observed with respect to a land-based reference frame. It is often contrasted with eustatic sea level, which is a measure of the total mass or volume of the oceans. Relative sea level can change by the processes changing eustatic sea level (e.g. ice melt and thermal expansion), but also by changes on land such as subsidence and isostatic rebound.

Past and future relative to the origin. For the grey areas a corresponding temporal classification is not possible. Straight lines passing the origin which are steeper than both photon world lines correspond with objects moving more slowly than the speed of light. If this applies to an object, then it applies from the viewpoint of all observers, because the world lines of these photons are the angle bisectors for any inertial reference frame.

A special class of accelerated observers follow worldlines whose three curvatures are constant. These motions belong to the class of Born rigid motions, i.e., the motions at which the mutual distance of constituents of an accelerated body or congruence remains unchanged in its proper frame. Two examples are Rindler coordinates or Kottler-Møller coordinates for the proper reference frame of hyperbolic motion, and Born or Langevin coordinates in the case of uniform circular motion.

The Erebus hotspot is a volcanic hotspot responsible for the high volcanic activity on Ross Island in the western Ross Sea of Antarctica. Its current eruptive zone, Mount Erebus, has erupted continuously since its discovery in 1841.Morgan, W.J.; Phipps Morgan, J. (2007) "Plate velocities in hotspot reference frame: electronic supplement". Magmas of the Erebus hotspot are similar to those erupted from hotspots at the active East African Rift in eastern Africa.

Ongoing work should resolve these issues in future releases. A guide for researchers using Gaia DR2, which collected "all information, tips and tricks, pitfalls, caveats, and recommendations relevant to" DR2, was prepared by the Gaia Helpdesk in December 2019. The coordinates in EDR3 will use a new Gaia celestial reference frame, which will be based on observations of about 1.5 million extragalactic sources and will be tied to the International Celestial Reference System.

Superselection rules, in short, are postulated rules forbidding the preparation of quantum states that exhibit coherence between eigenstates of certain observables. It was originally introduced to impose additional restriction to quantum theory beyond those of selection rules. As an example, superselection rules for electric charges disallow the preparation of a coherent superposition of different charge eigenstates. As it turns out, the lack of a reference frame is mathematically equivalent to superselection rules.

While selective and automatic, the ability of the machinery to selectively access inertial references within their field envelope is both remarkable as well as puzzling, since with this technology it would be possible to successfully begin construction of trans-luminal vessels, including the Thistledown itself. That the inhabitants did not is explained in the novels by the development of an extension of the selective inertial reference frame into a new 'pocket' universe: the Way.

However, in the Newtonian system the Galilean transformation connects these frames and in the special theory of relativity the Lorentz transformation connects them. The two transformations agree for speeds of translation much less than the speed of light. An example of the detection of a non-inertial, rotating reference frame is the precession of a Foucault pendulum. In the non-inertial frame of the Earth, the fictitious Coriolis force is necessary to explain observations.

GPS-IR was used in the Earthscope Plate Boundary Observatory. Larson also showed that it is possible to measure sea level changes, which allows the monitoring of subsidence and ground motion caused by earthquakes. These GPS receivers act as tide gauges, and can be tied to a terrestrial reference frame. She used them to monitor tidal levels in Kachemak Bay, and found that GPS was in good agreement with records from traditional tide gauges.

For example, the three planes could be one "face side" and two "datum edges". These three planes are marked A, B and C, where A is the face side, B is the first datum edge, and C is the second datum edge. In this case, the datum reference frame is A/B/C. A/B/C is shown at the end of feature control frame to show from where the measurement is taken.

NGS will release new datums in 2022. The North American Terrestrial Reference Frame of 2022 (NATRF2022) will supersede NAD83 in defining the geometric relationship between the North American plate and the ITRF. United States territories on the Pacific, Caribbean, and Mariana plates will have their own respective geodetic datums. The North American-Pacific Geopotential Datum of 2022 (NAPGD2022) will separately define the height system of the United States and its territories, replacing NAVD88.

During the turnaround, the traveling twin is in an accelerated reference frame. According to the equivalence principle, the traveling twin may analyze the turnaround phase as if the stay-at-home twin were freely falling in a gravitational field and as if the traveling twin were stationary. A 1918 paper by Einstein presents a conceptual sketch of the idea.Einstein, A. (1918) "dialog about objections against the theory of relativity", Die Naturwissenschaften 48, pp.

An updated reference frame ICRF2 was created in 2009. The update was a joint collaboration of the International Astronomical Union, the International Earth Rotation and Reference Systems Service, and the International VLBI Service for Geodesy and Astrometry. ICRF2 is defined by the position of 295 compact radio sources (97 of which also define ICRF1). Alignment of ICRF2 with ICRF1-Ext2, the second extension of ICRF1, was made with 138 sources common to both reference frames.

Including non-defining sources, it comprises 3414 sources measured using very-long-baseline interferometry. The ICRF2 has a noise floor of approximately 40 µas and an axis stability of approximately 10 µas. Maintenance of the ICRF2 will be accomplished by a set of 295 sources that have especially good positional stability and unambiguous spatial structure. The data used to derive the reference frame come from approximately 30 years of VLBI observations, from 1979 to 2009.

Since angles are invariant under transformations of reference frames, transforming back to the Earth's reference frame the result is still that the hunter should aim straight at the monkey. While this approach has the advantage of making the results intuitively obvious, it suffers from the slight logical blemish that the laws of classical mechanics are not postulated within the theory to be invariant under transformations to non-inertial (accelerated) reference frames (see also principle of relativity).

This resulted in an accurate but indirect link to an inertial, extragalactic, reference frame. Typical accuracies of the FK5, Hipparcos, Tycho-1, and Tycho-2 Catalogues as a function of time. Tycho-1 dependencies are shown for two representative magnitudes. For Tycho-2, a typical proper motion error of 2.5 milliarc-sec applies to both bright stars (positional error at J1991.25 of 7 milliarc-sec) and faint stars (positional error at J1991.25 of 60 milliarc-sec).

Hypothetical superluminal particles called tachyons have a spacelike trajectory, and thus can appear to move backward in time, according to an observer in a conventional reference frame. Despite frequent depiction in science fiction as a method to send messages back in time, tachyons do not interact with normal tardyonic matter in a way that would violate standard causality. Specifically, the Feinberg reinterpretation principle means that ordinary matter cannot be used to make a tachyon detector capable of receiving information.

Repeat TLS surveys allow the imaging and measurement of surface changes through time due, for example, to surface processes, volcanic deformation, ice flow, beach morphology transitions, and post-seismic slip. The incorporation of GPS measurements provides accurate georeferencing of TLS data in an absolute reference frame. The addition of digital photography yields photorealistic 3D images. It has been demonstrated that TLS derived 3D imagery is a unique and powerful tool for educational and outreach applications as well.

A more basic manifestation of the same effect involves two bodies that are falling side by side towards the Earth. In a reference frame that is in free fall alongside these bodies, they appear to hover weightlessly – but not exactly so. These bodies are not falling in precisely the same direction, but towards a single point in space: namely, the Earth's center of gravity. Consequently, there is a component of each body's motion towards the other (see the figure).

A celestial object's inclination indicates whether the object's orbit is prograde or retrograde. The inclination of a celestial object is the angle between its orbital plane and another reference frame such as the equatorial plane of the object's primary. In the Solar System, inclination of the planets is measured from the ecliptic plane, which is the plane of Earth's orbit around the Sun. The inclination of moons is measured from the equator of the planet they orbit.

Complex 3D city models typically are based on different sources of geodata such as geodata from GIS, building and site models from CAD and BIM. It is one of their core properties to establish a common reference frame for heterogeneous geo-spatial and geo- referenced data, i.e., the data need not to be merged or fused based on one common data model or schema. The integration is possible by sharing a common geo-coordinate system at the visualization level.

Stalling is an important phenomenon that affects the performance of the compressor. An analysis is made of rotating stall in compressors of many stages, finding conditions under which a flow distortion can occur which is steady in a traveling reference frame, even though upstream total and downstream static pressure are constant. In the compressor, a pressure-rise hysteresis is assumed. It is a situation of separation of air flow at the aero-foil blades of the compressor.

In footprint mapping a level, rectangular reference frame is placed around the base of the tree, to create a horizontal plane. The position of the multiple points on the trunk surface is measured with respect to the frame and plotted. This process repeated at different heights creating a series of virtual slices at different heights. The volume of each individual slice is then calculated and all are added together to determine the volume of the basal wedge.

Forces acting on an airplane in steady level longitudinal flight, also known as straight and level flight, with a very small angle of attack. In steady level longitudinal flight, thrust counterbalances drag and lift supports the aircraft's weight. Lift and drag are components of the aerodynamic force. Steady flight, unaccelerated flight, or equilibrium flight is a special case in flight dynamics where the aircraft's linear and angular velocity are constant in a body-fixed reference frame.

An overview can be found here. such as the equivalence of mass and energy transforming into one another and the resolution of the paradox that an excitation of the electromagnetic field could be viewed in one reference frame as electricity, but in another as magnetism. Einstein sought to generalize the invariance principle to all reference frames, whether inertial or accelerating. Rejecting Newtonian gravitation—a central force acting instantly at a distance—Einstein presumed a gravitational field.

Centrifugal force is an outward force apparent in a rotating reference frame. It does not exist when a system is described relative to an inertial frame of reference. All measurements of position and velocity must be made relative to some frame of reference. For example, an analysis of the motion of an object in an airliner in flight could be made relative to the airliner, to the surface of the Earth, or even to the Sun.

A child sliding down a slide at constant speed would be in mechanical equilibrium, but not in static equilibrium (in the reference frame of the earth or slide). Another example of mechanical equilibrium is a person pressing a spring to a defined point. He or she can push it to an arbitrary point and hold it there, at which point the compressive load and the spring reaction are equal. In this state the system is in mechanical equilibrium.

Earth's rotation period relative to the International Celestial Reference Frame, called its stellar day by the International Earth Rotation and Reference Systems Service (IERS), is seconds of mean solar time (UT1) , ). Earth's rotation period relative to the precessing mean vernal equinox, named sidereal day, is of mean solar time (UT1) , ). Thus, the sidereal day is shorter than the stellar day by about . Both the stellar day and the sidereal day are shorter than the mean solar day by about .

ITRF reference stations The International Terrestrial Reference System (ITRS) describes procedures for creating reference frames suitable for use with measurements on or near the Earth's surface. This is done in much the same way that a physical standard might be described as a set of procedures for creating a realization of that standard. The ITRS defines a geocentric system of coordinates using the SI system of measurement. An International Terrestrial Reference Frame (ITRF) is a realization of the ITRS.

The National Geodetic Survey is an office of NOAA's National Ocean Service. Its core function is to maintain the National Spatial Reference System (NSRS), "a consistent coordinate system that defines latitude, longitude, height, scale, gravity, and orientation throughout the United States". NGS is responsible for defining the NSRS and its relationship with the International Terrestrial Reference Frame (ITRF). The NSRS enables precise and accessible knowledge of where things are in the United States and its territories.

In physics, the Lorentz transformation (or Lorentz transformations) is named after the Dutch physicist Hendrik Lorentz. It was the result of attempts by Lorentz and others to explain how the speed of light was observed to be independent of the reference frame, and to understand the symmetries of the laws of electromagnetism. The Lorentz transformation is in accordance with special relativity, but was derived before special relativity. Early approximations of the transformation were published by Lorentz in 1895.

Apparent superluminal motion is observed in many radio galaxies, blazars, quasars, and recently also in microquasars. The effect was predicted before it was observed by Martin Rees and can be explained as an optical illusion caused by the object partly moving in the direction of the observer, when the speed calculations assume it does not. The phenomenon does not contradict the theory of special relativity. Corrected calculations show these objects have velocities close to the speed of light (relative to our reference frame).

General relativity was developed after special relativity to include concepts like gravity. It maintains the principle that no object can accelerate to the speed of light in the reference frame of any coincident observer. However, it permits distortions in spacetime that allow an object to move faster than light from the point of view of a distant observer. One such distortion is the Alcubierre drive, which can be thought of as producing a ripple in spacetime that carries an object along with it.

This relationship immediately highlights the fact that whether a static electromagnetic field is seen as purely magnetic, or purely electric, or some combination of these, is dependent upon one's reference frame (that is, one's velocity relative to the field). In ferromagnets, the movement creating the magnetic field is the electron spin (and to a lesser extent electron orbital angular momentum). In a current-carrying wire (electromagnets) the movement is due to electrons moving through the wire (whether the wire is straight or circular).

Walter 2007 In 1907 Einstein came to the conclusion that to achieve this a successor to special relativity was needed. From 1907 to 1915, Einstein worked towards a new theory, using his equivalence principle as a key concept to guide his way. According to this principle, a uniform gravitational field acts equally on everything within it and, therefore, cannot be detected by a free-falling observer. Conversely, all local gravitational effects should be reproducible in a linearly accelerating reference frame, and vice versa.

Geodetic Institute The Geodetic institute is the national authority for geodesy, determining the geodetic reference frame and other geodetic products such as the geoid and height reference. The institute operates a service for accurate GNSS- positioning. Mapping and Cadastre The Mapping and Cadastre establish and manage spatial data covering Norwegian land areas, in cooperation with municipalities and different public agencies. The division produce national map data series in different scales and the national printed map series Norway 1:50 000.

An Earth ellipsoid is a mathematical figure approximating the Earth's form, used as a reference frame for computations in geodesy, astronomy, and the geosciences. Various different ellipsoids have been used as approximations. It is an ellipsoid of revolution whose minor axis (shorter diameter), which connects the geographical North Pole and South Pole, is approximately aligned with the Earth's axis of rotation. The ellipsoid is defined by the equatorial axis a and the polar axis b; their difference is about 21 km, or 0.335%.

Notice that this will not work if the rotations are applied in any other order or if the airplane axes start in any position non-equivalent to the reference frame. Tait–Bryan angles, following z-y′-x″ (intrinsic rotations) convention, are also known as nautical angles, because they can be used to describe the orientation of a ship or aircraft, or Cardan angles, after the Italian mathematician and physicist Gerolamo Cardano, who first described in detail the Cardan suspension and the Cardan joint.

Another condition is that the speed of light must be independent of the reference frame, in practice of the velocity of the light source. Consider two inertial frames of reference O and O′, assuming O to be at rest while O′ is moving with a velocity v with respect to O in the positive x-direction. The origins of O and O′ initially coincide with each other. A light signal is emitted from the common origin and travels as a spherical wave front.

Background subtraction is a widely used approach for detecting moving objects in videos from static cameras. The rationale in the approach is that of detecting the moving objects from the difference between the current frame and a reference frame, often called "background image", or "background model". Background subtraction is mostly done if the image in question is a part of a video stream. Background subtraction provides important cues for numerous applications in computer vision, for example surveillance tracking or human pose estimation.

Horseshoe orbit of 2002 AA29. The graphic shows a full revolution of 95 years. The position of along the orbit is that of year 2003 (last nearest approach to Earth). Image: JPL If one looks at the orbit of from a point moving with the Earth around the Sun (the reference frame of the Earth–Sun system), it describes over the course of 95 years an arc of almost 360°, which during the next 95 years it retraces in reverse.

The location of the celestial poles of some selected Solar System objects is shown in the following table. The coordinates are given relative to Earth's celestial equator and the vernal equinox as they existed at J2000 (2000 January 1 12:00:00 TT) which is a plane fixed in inertial space now called the International Celestial Reference Frame (ICRF). Many poles precess or otherwise move relative to the ICRF, so their coordinates will change. The Moon's poles are particularly mobile.

An Introduction to the Mathematics of the Special Theory of Relativity, Springer, New York, It is clear that Whitehead respected these ideas, as may be seen for example in his 1919 book An Enquiry concerning the Principles of Natural KnowledgeWhitehead, A. N. (1919). An Enquiry concerning the Principles of Natural Knowledge, Cambridge University Press, Cambridge UK. as well as in Process and Reality. In this view, time is relative to an inertial reference frame, different reference frames defining different versions of time.

For instance, see 0.4 and 0.5 of (Ricci 2007) The link between these two conditions is given by the identity [\chi(a)]_m=[\eta(m)]_a, which holds for all m and all algebra elements a.For instance, see 0.4 (E) of (Ricci 2007) Several other conditions that characterize bases for universal algebras are omitted. As the next example will show, present bases are a generalization of the bases of vector spaces. Then, the name "reference frame" can well replace "basis".

A reference frame that is at rest (or one that moves with no rotation and at constant velocity) relative to the "fixed stars" is generally taken to be an inertial frame. Any system can be analyzed in an inertial frame (and so with no centrifugal force). However, it is often more convenient to describe a rotating system by using a rotating frame—the calculations are simpler, and descriptions more intuitive. When this choice is made, fictitious forces, including the centrifugal force, arise.

"Curious About Astronomy?" , Cornell University, retrieved June 2007 In the Earth reference frame (in which the object being weighed is at rest), the object does not appear to be accelerating, however the two real forces, gravity and the force from the spring, are the same magnitude and do not balance. The centrifugal force must be included to make the sum of the forces be zero to match the apparent lack of acceleration. Note: In fact, the observed weight difference is more — about 0.53%.

The conception of centrifugal force has evolved since the time of Huygens, Newton, Leibniz, and Hooke who expressed early conceptions of it. Its modern conception as a fictitious force arising in a rotating reference frame evolved in the eighteenth and nineteenth centuries. Centrifugal force has also played a role in debates in classical mechanics about detection of absolute motion. Newton suggested two arguments to answer the question of whether absolute rotation can be detected: the rotating bucket argument, and the rotating spheres argument.

Unlike former astronomical time scales, TCG is defined in the context of the general theory of relativity. The relationships between TCG and other relativistic time scales are defined with fully general relativistic metrics. Because the reference frame for TCG is not rotating with the surface of the Earth and not in the gravitational potential of the Earth, TCG ticks faster than clocks on the surface of the Earth by a factor of about 7.0 × 10−10 (about 22 milliseconds per year).

It is inspired by the key idea behind special relativity, that the details of an observation depend on the reference frame of the observer, and uses some ideas from Wheeler on quantum information.Wheeler (1990): pg. 3 The physical content of the theory has not to do with objects themselves, but the relations between them. As Rovelli puts it: > "Quantum mechanics is a theory about the physical description of physical > systems relative to other systems, and this is a complete description of the > world".

The MicroGravity Test Facility (MGTF) facilitates testing of a single mobile SPHERES satellite, using six degrees-of-freedom. In this, the unit is held by a gimbal with 3 DoF, which is suspended from a translation crane with 3 DoF. The laboratory is able to provide a navigational reference frame in a similar configuration as in the International Space Station using five ultrasonic beacons, and the output of cold gas thrusters are analysed to simulate the expected movement in a micro-gravity environment.

A basic rotation (also called elemental rotation) is a rotation about one of the axes of a coordinate system. The following three basic rotation matrices rotate vectors by an angle about the -, -, or -axis, in three dimensions, using the right-hand rule—which codifies their alternating signs. (The same matrices can also represent a clockwise rotation of the axes.Note that if instead of rotating vectors, it is the reference frame that is being rotated, the signs on the terms will be reversed.

The slight overpopulation of one orientation means that a residual dipolar coupling remains to be observed. The dipolar coupling is commonly used in solid state NMR and provides information about the relative orientation of the bond vectors relative to a single global reference frame. Typically the orientation of the N-H vector is probed in an HSQC-like experiment. Initially, residual dipolar couplings were used for refinement of previously determined structures, but attempts at de novo structure determination have also been made.

Maxwell's equations were an essential inspiration for Einstein's development of special relativity. Possibly the most important aspect was their denial of instantaneous action at a distance. Rather, according to them, forces are propagated at the velocity of light through the electromagnetic field. Maxwell's original equations are based on the idea that light travels through a sea of molecular vortices known as the "luminiferous aether", and that the speed of light has to be respective to the reference frame of this aether.

De Broglie supposed that every particle was associated with both a particle and a wave. The angular frequency \omega and wavenumber k of the wave was related to the energy E and momentum p of the particle by : E=\hbar \omega and : p=\hbar k . The question reduces to whether every observer in every inertial reference frame can agree on the phase of the wave. If so, then a wave-like description of particles may be consistent with special relativity.

Angular Correlation of Electron Positron Annihilation Radiation (ACAR or ACPAR) is a technique of solid state physics to investigate the electronic structure of metals. It uses positrons which are implanted into a sample and annihilate with the electrons. In the majority of annihilation events, two gamma quanta are created that are, in the reference frame of the electron- positron pair, emitted in exactly opposite directions. In the laboratory frame, there is a small angular deviation from collinearity, which is caused by the momentum of the electron.

Polar wander is the motion of a pole in relation to some reference frame. It can be used, for example, to measure the degree to which Earth's magnetic poles have been observed to move relative to the Earth's rotation axis. It is also possible to use continents as reference and observe the relative motion of the magnetic pole relative to the different continents; by doing so, the relative motion of those two continents to each other can be observed over geologic time as paleomagnetism.

If the near light-speed space craft is interacting with matter or energy that is moving slowly in the planetary reference frame—solar wind, magnetic fields, cosmic microwave background radiation—this will cause drag which will bleed off a portion of the engine's acceleration. A second big issue facing ships using constant acceleration for interstellar travel is colliding with matter and radiation while en route. In mid-journey any matter the ship strikes will be impacting at near light speed, so the impact will be dramatic.

The movement of each of the components of the Boulton & Watt Steam Engine (1784) is modeled by a continuous set of rigid displacements. The position of one component of a mechanical system relative to another is defined by introducing a reference frame, say M, on one that moves relative to a fixed frame, F, on the other. The rigid transformation, or displacement, of M relative to F defines the relative position of the two components. A displacement consists of the combination of a rotation and a translation.

Unlike the inertial force or fictitious force known as centrifugal force, which always exists in addition to the reactive force in the rotating frame of reference, the reactive force is a real Newtonian force that is observed in any reference frame. The two forces will only have the same magnitude in the special cases where circular motion arises and where the axis of rotation is the origin of the rotating frame of reference. It is the reactive force that is the subject of this article.

Covers late 1899 through 2049. DE402 was released in 1995, and was quickly superseded by DE403. DE403 was created 1993, released in 1995, expressed in the coordinates of the International Earth Rotation Service (IERS) reference frame, essentially the ICRF. The data compiled by JPL to derive the ephemeris began to move away from limited-accuracy telescopic observations and more toward higher-accuracy radar-ranging of the planets, radio-ranging of spacecraft, and very-long-baseline-interferometric (VLBI) observations of spacecraft, especially for the four inner planets.

This concept of time and simultaneity was later generalized by Einstein in his special theory of relativity (1905) where he developed transformations between inertial frames of reference based upon the universal nature of physical laws and their economy of expression (Lorentz transformations). The definition of inertial reference frame can also be extended beyond three-dimensional Euclidean space. Newton's assumed a Euclidean space, but general relativity uses a more general geometry. As an example of why this is important, consider the geometry of an ellipsoid.

The movement of a rigid body, such as a plate, on the surface of a sphere can be described as rotation about a fixed axis (relative to the chosen reference frame). This pole of rotation is known as an Euler pole. The movement of a plate is completely specified in terms of its Euler pole and the angular rate of rotation about the pole. Euler poles defined for current plate motions can be used to reconstruct plates in the recent past (few million years).

Consider a three-dimensional space with unit basis vectors A, B, and C. The sphere in the figure below is used to show the scale of the reference frame for context and the box is used to provide a rotational context. ABC unit basis vectors. Typically, in electrical engineering (or any other context that uses three-phase systems), the three-phase components are shown in a two- dimensional perspective. However, given the three phases can change independently, they are by definition orthogonal to each other.

This enables us to add a time-dependent term to the dipole expression. The modulation of this term is 1 year, which fits the observation done by COBE FIRAS. The dipole moment does not encode any primorial information. From the CMB data, it is seen that the earth appears to be moving at 368±2 km/s relative to the reference frame of the CMB (also called the CMB rest frame, or the frame of reference in which there is no motion through the CMB.).

Precession of a gyroscope Precession is a change in the orientation of the rotational axis of a rotating body. In an appropriate reference frame it can be defined as a change in the first Euler angle, whereas the third Euler angle defines the rotation itself. In other words, if the axis of rotation of a body is itself rotating about a second axis, that body is said to be precessing about the second axis. A motion in which the second Euler angle changes is called nutation.

A garnet porphyroblast (black) contains curved trails of small inclusions (white and grey). Some garnet porphyroblasts contain curving trails of quartz and other mineral inclusions that record rotation of the crystals relative to their surroundings. However, the question of how much porphyroblasts actually rotate in an external reference frame fixed to the Earth's surface during metamorphism and deformation has long been the subject of debate. The question focused on so-called "spiral garnets", also known as "snowball garnets", whose inclusion trails define spiral patterns.

In the same year, P-wave data were used to determine 150 spherical harmonic coefficients for velocity anomalies in the mantle. The first model using iterative techniques, required when there are a large numbers of unknowns, was done in 1984. This built upon the first radially anisotropic model of the Earth, which provided the required initial reference frame to compare tomographic models to for iteration. Initial models had resolution of ~3000 to 5000 km, as compared to the few hundred kilometer resolution of current models.

The Geometry of Minkowski Spacetime. An Introduction to the Mathematics of the Special Theory of Relativity, Springer, New York, It is clear that Whitehead respected these ideas, as may be seen for example in his 1919 book An Enquiry concerning the Principles of Natural KnowledgeWhitehead, A.N. (1919). An Enquiry concerning the Principles of Natural Knowledge, Cambridge University Press, Cambridge UK. as well as in Process and Reality. Time in this view is relative to an inertial reference frame, different reference frames defining different versions of time.

The ICRF, now called ICRF1, was adopted by the International Astronomical Union (IAU) on 1 January 1998. ICRF1 had an angular noise floor of approximately 250 microarcseconds (µas) and a reference axis stability of approximately 20 µas; this was an order-of- magnitude improvement over the previous reference frame derived from Fifth Fundamental Catalog (FK5). The ICRF1 contains 212 defining sources and also contains positions of 396 additional non-defining sources for reference. The positions of these sources have been adjusted in later extensions to the catalogue.

Clumped isotopes present a distinct set of challenges for isotopic reference materials. By convention the clumped isotope composition of CO2 liberated from CaCO3 (Δ47) and CH4 (Δ18/Δ13CH3D/Δ12CH2D2) are reported relative to a stochastic distribution of isotopes. That is, the ratio of a given isotopologue of a molecule with multiple isotopic substitutions against a reference isotopologue is reported normalized to that same abundance ratio where all isotopes are distributed randomly. In practice the chosen reference frame is almost always the isotopologue with no isotopic substitutions.

Inertial navigation systems used a cluster of gyroscopes and accelerometers to determine accelerations relative to inertial space. After a gyroscope is spun up in a particular orientation in inertial space, the law of conservation of angular momentum requires that it retain that orientation as long as no external forces are applied to it. Three orthogonal gyroscopes establish an inertial reference frame, and the accelerators measure acceleration relative to that frame. The accelerations, along with a clock, can then be used to calculate the change in position.

Systems that have nonzero energy but zero rest mass (such as photons moving in a single direction, or equivalently, plane electromagnetic waves) do not have COM frames, because there is no frame in which they have zero net momentum. Due to the invariance of the speed of light, a massless system must travel at the speed of light in any frame, and always possesses a net momentum. Its energy is—for each reference frame—equal to the magnitude of momentum multiplied by the speed of light: : E = p c .

In physics, the laboratory frame of reference, or lab frame for short, is a frame of reference centered on the laboratory in which the experiment (either real or thought experiment) is done. This is the reference frame in which the laboratory is at rest. Also, this is usually the frame of reference in which measurements are made, since they are presumed (unless stated otherwise) to be made by laboratory instruments. An example of instruments in a lab frame, would be the particle detectors at the detection facility of a particle accelerator.

The rate at which two objects in motion in a single frame of reference get closer together is called the mutual or closing speed. This may approach twice the speed of light, as in the case of two particles travelling at close to the speed of light in opposite directions with respect to the reference frame. Imagine two fast-moving particles approaching each other from opposite sides of a particle accelerator of the collider type. The closing speed would be the rate at which the distance between the two particles is decreasing.

A rotation matrix, on the other hand, provides a full description of the attitude at the expense of requiring nine values instead of three. The use of a rotation matrix can lead to increased computational expense and they can be more difficult to work with. Quaternions offer a decent compromise in that they do not suffer from gimbal lock and only require four values to fully describe the attitude. Changing orientation of a rigid body is the same as rotating the axes of a reference frame attached to it.

The term "Lorentz transformations" only refers to transformations between inertial frames, usually in the context of special relativity. In each reference frame, an observer can use a local coordinate system (usually Cartesian coordinates in this context) to measure lengths, and a clock to measure time intervals. An event is something that happens at a point in space at an instant of time, or more formally a point in spacetime. The transformations connect the space and time coordinates of an event as measured by an observer in each frame.

The first definition of such a filter is already found in the H.263 standard, though, and Golden Frames were already in use in VP5 and VP7. The discrete cosine transform (DCT) on 4×4 blocks and the Hadamard transform (WHT) serve as basic frequency transforms. A maximum of three frames can be referenced for temporal prediction: the last Golden Frame (may be an intra frame), alternate reference frame, and the directly preceding frame. The so-called alternate reference frames (altref) can serve as reference-only frames for displaying them can be deactivated.

In this case the encoder can fill them with arbitrary useful image data, even from future frames, and thereby serve the same purpose as the b-frames of the MPEG formats. Similar macroblocks can be assigned to one of up to four (even spatially disjoint) segments and thereby share parameters like the reference frame used, quantizer step size, or filter settings. VP8 offers two different adjustable deblocking filters that are integrated into the codec loops (in- loop filtering). Many coding tools use probabilities that are calculated continuously from recent context, starting at each intra frames.

A macroscopic body that is stationary (i.e. a reference frame has been chosen to correspond to the body's center of momentum) may have various kinds of internal energy at the molecular or atomic level, which may be regarded as kinetic energy, due to molecular translation, rotation, and vibration, electron translation and spin, and nuclear spin. These all contribute to the body's mass, as provided by the special theory of relativity. When discussing movements of a macroscopic body, the kinetic energy referred to is usually that of the macroscopic movement only.

Plot of velocity parameters and times on the horizontal axis, versus position on the vertical axis, for an accelerated twin roundtrip to a destination with ΔxAB=10c2/α ~10 lightyears away if α~9.8 m/s2. From the frame of reference of those on the ship the acceleration will not change as the journey goes on. Instead the planetary reference frame will look more and more relativistic. This means that for voyagers on the ship the journey will appear to be much shorter than what planetary observers see.

Another requirement is that the parties have access to a common reference frame, so that they can guarantee that some communication events are spacelike separated. In relativistic cryptography, it is assumed that each party participating in the cryptographic task has various trusted agents that collaborate to implement the task. The agents implement the protocol by performing different actions at various points in spacetime. The agents of the same party may communicate via authenticated and secure channels, which can be implemented with previously shared secure keys, for example using one-time pads.

Attitude control (3-axis stabilization) is achieved using two 3-axis inertial measurement units, a set of two star cameras and two Sun sensors, gyroscopes, accelerometers, and four 12 N·m·s reaction wheels. Pointing accuracy is 0.04 degree with respect to the inertial reference frame and 0.8 degree with respect to the Mars orbital frame. Three on-board systems help Mars Express maintain a very precise pointing accuracy, which is essential to allow the spacecraft to communicate with a 35-metre and 70-metre dish on Earth up to 400 million kilometres away.

Changing orientation of a rigid body is the same as rotating the axes of a reference frame attached to it. In geometry, the orientation, angular position, attitude, or direction of an object such as a line, plane or rigid body is part of the description of how it is placed in the space it occupies. More specifically, it refers to the imaginary rotation that is needed to move the object from a reference placement to its current placement. A rotation may not be enough to reach the current placement.

Mach's principle is the name given by Einstein to a hypothesis often credited to the physicist and philosopher Ernst Mach. The idea is that the local motion of a rotating reference frame is determined by the large-scale distribution of matter in the universe. Mach's principle says that there is a physical law that relates the motion of the distant stars to the local inertial frame. If you see all the stars whirling around you, Mach suggests that there is some physical law which would make it so you would feel a centrifugal force.

For a single body in an empty universe, motion of any kind is inconceivable. Because rotation does not exist, centrifugal force does not exist. Of course, addition of a speck of matter just to establish a reference frame cannot cause the sudden appearance of centrifugal force, so it must be due to rotation relative to the entire mass of the universe. The modern view is that centrifugal force is indeed an indicator of rotation, but relative to those frames of reference that exhibit the simplest laws of physics.

Hotspots are sites of upwelling of relatively hot mantle, possibly associated with mantle plumes, that cause partial melting of the asthenosphere. This type of magmatism forms volcanic seamounts or oceanic islands when they become emergent. Over short geological timescales the hotspots appear to be fixed relative to one another, forming a reference frame against which plate motions can be measured. As tectonic plates move relative to a hotspot, the location of magmatic activity on the plate shifts, causing the development of time-progressive chains of volcanoes such as the Hawaiian–Emperor seamount chain.

Furthermore, the poor accuracy for detecting features of the object on the left side of the object's axis was more severe when the objects were presented on the contralesional side of the body. Thus, these findings illustrate that both allocentric and egocentric biases are present simultaneously, and that egocentric information can influence the severity of allocentric neglect. A second study, conducted by Moscovitch and Behrmann, investigated the reference frame of neglect with respect to the somatosensory system. Eleven patients with parietal lobe lesions and subsequent hemispatial neglect were analyzed during this experiment.

The effect can be understood in two ways, depending on the reference frame chosen. Radiation from a star (S) and thermal radiation from a particle seen (a) from an observer moving with the particle and (b) from an observer at rest with respect to the star. From the perspective of the grain of dust circling a star (panel (a) of the figure), the star's radiation appears to be coming from a slightly forward direction (aberration of light). Therefore the absorption of this radiation leads to a force with a component against the direction of movement.

Here Copernicus asserts that the motion of the equinoxes and celestial poles has not been uniform, and argues that consequently they should not be used to define the reference frame with respect to which the motions of the planets are measured, and that the periods of the various planetary motions are more accurately determinable if those motions are measured with respect to the fixed stars. He maintains that he had found the length of the sidereal year to have always been 365 days 6 hours and 10 minutes.

The Scotia Plate () is a tectonic plate on the edge of the South Atlantic and Southern Ocean. Thought to have formed during the early Eocene with the opening of the Drake Passage that separates South America from Antarctica, it is a minor plate whose movement is largely controlled by the two major plates that surround it: the South American Plate and Antarctic Plate. Roughly rhomboid, extending between and , the plate is wide and long. It is moving WSW at /year and the South Sandwich Plate is moving east at /year in an absolute reference frame.

Einstein-aether theories were popularized by Maurizio Gasperini in a series of papers, such as Singularity Prevention and Broken Lorentz Symmetry in the 1980s. In addition to the metric of general relativity these theories also included a scalar field which intuitively corresponded to a universal notion of time. Such a theory will have a preferred reference frame, that in which the universal time is the actual time. The dynamics of the scalar field is identified with that of an aether which is at rest in the preferred frame.

This mathematical concept is closely related to the description of fluid motion—its kinematics and dynamics—in a Lagrangian frame of reference. In this reference frame, fluid parcels are labelled and followed through space and time. But also in the Eulerian frame of reference the notion of fluid parcels can be advantageous, for instance in defining the material derivative, streamlines, streaklines, and pathlines; or for determining the Stokes drift. The fluid parcels, as used in continuum mechanics, are to be distinguished from microscopic particles (molecules and atoms) in physics.

Although the new geographic coordinate system LV95 was introduced in 1995, it was only progressively brought to use by Swiss authorities, with the official deadline for its definitive implementation having been fixed for the year 2016. Nowadays the LV95 system has become the main geographic reference frame of various institutions and governmental agencies, such as the Federal Statistical Office, the Swiss Army and the Swiss Border Guard, as well as cantonal police corps, emergency services and cadastre offices. Likewise, the official National Maps of Switzerland are now also founded upon this new coordinate system.

For instance, if one observer notes that a particle collides with the center of a bullseye, then all observers must reach the same conclusion. This requirement places constraints on the nature of electromagnetic fields and on their transformation from one reference frame to another. It also places constraints on the manner in which fields affect the acceleration and, hence, the trajectories of charged particles. Perhaps the simplest example, and one that Einstein referenced in his 1905 paper introducing special relativity, is the problem of a conductor moving in the field of a magnet.

Spacetime wave packets are a form of spatially correlated light that seems to violate the normal physical rules applying to light beams. In particular, their group velocity in free space can differ from the normal speed of light in vacuum. and their behavior under refraction does not follow the normal expectations given by Snell's law. Monochromatic Gaussian beam is shown to be transformed into spacetime wave packets under Lorentz transformation, thus any monochromatic Gaussian beam observed in a reference frame moving at relativistic velocity appears as spacetime wave packets.

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 physical object or particle moving faster than the speed of light would have space-like four-momenta (such as the hypothesized tachyon), and these do not appear to exist. Any time-like four- momentum possesses a reference frame where the momentum (3-dimensional) is zero, which is a center of momentum frame. In this case, invariant mass is positive and is referred to as the rest mass. If objects within a system are in relative motion, then the invariant mass of the whole system will differ from the sum of the objects' rest masses.

This theory, now known as ZND theory, admits finite-rate chemical reactions and thus describes a detonation as an infinitesimally thin shock wave followed by a zone of exothermic chemical reaction. With a reference frame of a stationary shock, the following flow is subsonic, so that an acoustic reaction zone follows immediately behind the lead front, the Chapman-Jouguet condition. Continued in Continued in There is also some evidence that the reaction zone is semi- metallic in some explosives. Both theories describe one-dimensional and steady wave fronts.

A practical application of the Coriolis effect is the mass flow meter, an instrument that measures the mass flow rate and density of a fluid flowing through a tube. The operating principle involves inducing a vibration of the tube through which the fluid passes. The vibration, though not completely circular, provides the rotating reference frame that gives rise to the Coriolis effect. While specific methods vary according to the design of the flow meter, sensors monitor and analyze changes in frequency, phase shift, and amplitude of the vibrating flow tubes.

In collaboration with Charles Bennett and Gilles Brassard, he made a significant early contribution to quantum cryptography. Starting in 2012, he has advocated the interpretation known as Quantum Bayesianism, or QBism. In 2003, the journal Foundations of Physics published a bibliography of Mermin's writing that included three books, 125 technical articles, 18 pedagogical articles, 21 general articles, 34 book reviews, and 24 "Reference Frame" articles from Physics Today. Mermin was elected a Fellow of the American Physical Society in 1969, and he was elected a member of the National Academy of Sciences in 1991.

These microstructures are interpreted classically as having formed by shearing induced rotation of a growing garnet crystal. Later research, however, led to an alternative formation model in which a porphyroblast grows over a developing microfold while maintaining a stable position in the external reference frame. Repetition of this process can then produce complex spiral-shaped patterns. Although many researchers continue to adopt the classic rotational model, most researchers who have published research testing both models by measuring the orientations of porphyroblasts have come to support the modern interpretation.

One becomes more consciously involved with members of his/her own ethnic group to the exclusion of those from other groups. This stage is often marked by a full-fledged immersion into Black culture and a Black reference frame, and a subsequent emersion from the oversimplified, and often racist immersion experience that floods the early part of this stage. Eventually, the individual's highly emotional response to the encounter begins to plateau and this “psychological defensiveness” is replaced by “affective and cognitive openness,” which allows for a more critical analysis and worldview formation.

TCG is defined by a different reference frame from TCB, such that they are not linearly related. Over the long term, TCG ticks more slowly than TCB by about 1.6 × 10−8 (about 0.5 seconds per year). In addition there are periodic variations, as Earth moves within the Solar system. When the Earth is at perihelion in January, TCG ticks even more slowly than it does on average, due to gravitational time dilation from being deeper in the Sun's gravity well and also velocity time dilation from moving faster relative to the Sun.

In a rotational mechanical equilibrium the angular momentum of the object is conserved and the net torque is zero. More generally in conservative systems, equilibrium is established at a point in configuration space where the gradient of the potential energy with respect to the generalized coordinates is zero. If a particle in equilibrium has zero velocity, that particle is in static equilibrium. Since all particles in equilibrium have constant velocity, it is always possible to find an inertial reference frame in which the particle is stationary with respect to the frame.

SPHERES satellites determine their position and attitude by using 23 on-board ultrasonic receivers (Murata MA40S4R) and 5 external ultrasonic reference beacons. The ultrasonic time-of-flight measurements from the external beacons to the on-board receivers are used to calculate the satellite's position with respect to the external reference frame. For rapid determination of position, the ultrasonic time-of-flight information is supplemented with the data from on-board accelerometers (3x Honeywell QA-750 single-axis accelerometers) and gyroscopes (3x Systron Donner QRS14 single-axis rate gyroscopes).

Einstein generalized relativity to frames of reference that were non-inertial. He achieved this by positing the Equivalence Principle, which states that the force felt by an observer in a given gravitational field and that felt by an observer in an accelerating frame of reference are indistinguishable. This led to the conclusion that the mass of an object warps the geometry of the space-time surrounding it, as described in Einstein's field equations. In classical physics, an inertial reference frame is one in which an object that experiences no forces does not accelerate.

The orientation of the BCRS coordinate system coincides with that of the International Celestial Reference System (ICRS). Both are centered at the barycenter of the Solar System, and both "point" in the same direction. That is, their axes are aligned with that of the International Celestial Reference Frame (ICRF), which was adopted as a standard by the IAU two years earlier (1998). The motivation of the ICRF is to define what "direction" means in space, by fixing its orientation in relation to the Celestial sphere, that is, to deep-space background.

WGS 84 Implementation Manual page i, 1998 Tectonic plates slowly move over the surface of Earth, so most countries have adopted for their maps an IRM version fixed relative to their own tectonic plate as it existed at the beginning of a specific year. Examples include the North American Datum 1983 (NAD83), the European Terrestrial Reference Frame 1989 (ETRF89), and the Geocentric Datum of Australia 1994 (GDA94). Versions fixed to a tectonic plate differ from the global version by at most a few centimetres. However, the IRM is not fixed to any point on Earth.

A vector loop must obey certain modeling rules as it passes through a part. It must: # enter through a joint, # follow the datum path to the Datum Reference Frame (DRF), # follow a second datum path leading to another joint, and # exit to the next adjacent part in the assembly. Additional modeling rules for vector loops include: # Loops must pass through every part and every joint in the assembly. # A single vector loop may not pass through the same part or the same joint twice, but it may start and end in the same part.

Global motion compensation describes the motion in a scene based on a single affine transform instruction. The reference frame is panned, rotated and zoomed in accordance to GMC warp points to create a prediction of how the following frame will look. Since this operation works on individual pixels (rather than blocks), it is capable of creating predictions that are not possible using block-based approaches. Each macroblock in such a frame can be compensated using global motion (no further motion information is then signalled) or, alternatively, local motion (as if GMC were off).

In 2010 this dish was used for several Very Long Baseline Interferometry observationsTzioumis et al, Evolution of the pc- scale structure of PKS 1934-638 revisited: first science with the ASKAP and New Zealand telescopes, The Astronomical Journal 140 (2010) 1506-1510 as part of the Australian Long Baseline Array. It will also from 2011 be part of the International VLBI Service for Geodesy and Astrometry. As such, it is also co- located with a LINZ/GeoNet 'PositioNZ' GNSS station to help future inclusion in the definition of the International Terrestrial Reference Frame (ITRF).

However, the principle of special relativity generalizes the notion of inertial frame to include all physical laws, not simply Newton's first law. Newton viewed the first law as valid in any reference frame that is in uniform motion relative to the fixed stars;The question of "moving uniformly relative to what?" was answered by Newton as "relative to absolute space". As a practical matter, "absolute space" was considered to be the fixed stars. For a discussion of the role of fixed stars, see that is, neither rotating nor accelerating relative to the stars.

A variety of methods to establish this reference frame link before catalogue publication were included and appropriately weighted: interferometric observations of radio stars by VLBI networks, MERLIN and VLA; observations of quasars relative to Hipparcos stars using CCDs, photographic plates, and the Hubble Space Telescope; photographic programmes to determine stellar proper motions with respect to extragalactic objects (Bonn, Kiev, Lick, Potsdam, Yale/San Juan); and comparison of Earth rotation parameters obtained by VLBI and by ground- based optical observations of Hipparcos stars. Although very different in terms of instruments, observational methods and objects involved, the various techniques generally agreed to within 10 milliarc-sec in the orientation and 1 milliarc-sec/year in the rotation of the system. From appropriate weighting, the coordinate axes defined by the published catalogue are believed to be aligned with the extragalactic radio frame to within ±0.6 milliarc-sec at the epoch J1991.25, and non-rotating with respect to distant extragalactic objects to within ±0.25 milliarc-sec/yr. The Hipparcos and Tycho Catalogues were then constructed such that the Hipparcos reference frame coincides, to within observational uncertainties, with the International Celestial Reference System (the ICRS), and representing the best estimates at the time of the catalogue completion (in 1996).

For a calorically perfect gas such as an ideal gas, the enthalpy is directly proportional to the temperature, and this leads to the concept of the total (or stagnation) temperature. When shock waves are present, in a reference frame in which the shock is stationary and the flow is steady, many of the parameters in the Bernoulli equation suffer abrupt changes in passing through the shock. The Bernoulli parameter itself, however, remains unaffected. An exception to this rule is radiative shocks, which violate the assumptions leading to the Bernoulli equation, namely the lack of additional sinks or sources of energy.

Another field measurement approach, using an Eulerian reference frame, is to capture various properties of the lake water (including mass movement, water temperature, electrical conductivity and levels of dissolved substances, typically oxygen) at various fixed positions in the lake. From these can be constructed an understanding of the dominant processes operating in the various parts of the lake and their range and duration. Field measurements alone are usually not a reliable basis for generating residence times, mainly because they necessarily represent a small subset of locations and conditions. Therefore, the measurements are generally used as the input for numerical models.

As this can only occur in one reference frame in Newtonian physics (see Galilean relativity), the aether was hypothesized as the absolute and unique frame of reference in which Maxwell's equations hold. That is, the aether must be "still" universally, otherwise c would vary along with any variations that might occur in its supportive medium. Maxwell himself proposed several mechanical models of aether based on wheels and gears, and George Francis FitzGerald even constructed a working model of one of them. These models had to agree with the fact that the electromagnetic waves are transverse but never longitudinal.

In classical mechanics, the Euler acceleration (named for Leonhard Euler), also known as azimuthal acceleration or transverse acceleration is an acceleration that appears when a non-uniformly rotating reference frame is used for analysis of motion and there is variation in the angular velocity of the reference frame's axis. This article is restricted to a frame of reference that rotates about a fixed axis. The Euler force is a fictitious force on a body that is related to the Euler acceleration by F = ma, where a is the Euler acceleration and m is the mass of the body.

Euler also realized that the composition of two rotations is equivalent to a single rotation about a different fixed axis (Euler's rotation theorem). Therefore, the composition of the former three angles has to be equal to only one rotation, whose axis was complicated to calculate until matrices were developed. Based on this fact he introduced a vectorial way to describe any rotation, with a vector on the rotation axis and module equal to the value of the angle. Therefore, any orientation can be represented by a rotation vector (also called Euler vector) that leads to it from the reference frame.

These angles are normally taken as one in the external reference frame (heading, bearing), one in the intrinsic moving frame (bank) and one in a middle frame, representing an elevation or inclination with respect to the horizontal plane, which is equivalent to the line of nodes for this purpose. For an aircraft, they can be obtained with three rotations around its principal axes if done in the proper order. A yaw will obtain the bearing, a pitch will yield the elevation and a roll gives the bank angle. Therefore, in aerospace they are sometimes called yaw, pitch and roll.

Euler also realized that the composition of two rotations is equivalent to a single rotation about a different fixed axis (Euler's rotation theorem). Therefore, the composition of the former three angles has to be equal to only one rotation, whose axis was complicated to calculate until matrices were developed. Based on this fact he introduced a vectorial way to describe any rotation, with a vector on the rotation axis and module equal to the value of the angle. Therefore, any orientation can be represented by a rotation vector (also called Euler vector) that leads to it from the reference frame.

A third idea for potentially solving the distant starlight problem, put forward by Russell Humphreys in 1994 and refined by others since, sets this assumption aside and proposes that the Earth is located near the center of a finite and bounded (i.e. spherical) universe. Time dilation would have allowed billions of years of time to elapse at the edge of the universe in its own reference frame, while only a few days passed on Earth. Humphreys also finds a place for the "waters above (and below) the Earth," locating them at the edge ("above") and the centre ("below") of the universe.

The patient performed a series of tasks such as the Moscovitch Letter Manipulation Task, the Brooks Matrix Task, and a Compass Directions Task. The patient proved able to receive the spatial material well with short-term memory when manipulating materials without a reference frame. The patient was still able to make global processes, identify shapes, single lines, and letters, but lacked the ability to process configurations in perceptual representations, in the respective tasks. When visually holding an image for 10 seconds, the patient was able to process a spatial pattern and transfer that image onto paper accurately.

Grand Prix motorcyclist leaning in a turn inertial, acting on a leaning bike in the rotating reference frame of a turn where N is the normal force, Ff is friction, m is mass, r is turn radius, v is forward speed, and g is the acceleration of gravity. Graph of bike lean angle vs forward speed, assuming unlimited friction between tires and ground. Cyclist riding with no hands on the handlebars. In order for a bike to turn, that is, change its direction of forward travel, the front wheel must aim approximately in the desired direction, as with any front-wheel steered vehicle.

A coordinate time scale (or coordinate time standard) is a time standard designed for use as the time coordinate in calculations that need to take account of relativistic effects. The choice of a time coordinate implies the choice of an entire frame of reference. As described above, a time coordinate can to a limited extent be illustrated by the proper time of a clock that is notionally infinitely far away from the objects of interest and at rest with respect to the chosen reference frame. This notional clock, because it is outside all gravity wells, is not influenced by gravitational time dilation.

The Golden Rule was one of several fiscal policy principles set out by the incoming Labour government in 1997. These were first set out by then Chancellor of the Exchequer Gordon Brown in his 1997 budget speech. Subsequently they were formalised in the Finance Act 1998 and in the Code for Fiscal Stability, approved by the House of Commons in December 1998. In 2005 there was speculation that the Chancellor had manipulated these rules as the treasury had moved the reference frame for the start of the economic cycle to two years earlier (from 1999 to 1997).

IMUs are often incorporated into Inertial Navigation Systems which utilize the raw IMU measurements to calculate attitude, angular rates, linear velocity and position relative to a global reference frame. The IMU equipped INS forms the backbone for the navigation and control of many commercial and military vehicles such as manned aircraft, missiles, ships, submarines, and satellites. IMUs are also essential components in the guidance and control of unmanned systems such as UAVs, UGVs, and UUVs. Simpler versions of INSs termed Attitude and Heading Reference Systems utilize IMUs to calculate vehicle attitude with heading relative to magnetic north.

The fallacy with this critic's argument was, as demonstrated in section Point of null frequency shift, that it is simply not true that a Doppler shift must always be observed between two frames in uniform relative motion. Furthermore, as demonstrated in section Source and receiver are at their points of closest approach, the difficulty of analyzing a relativistic scenario often depends on the choice of reference frame. Attempting to analyze the scenario in the frame of the receiver involves much tedious algebra. It is much easier, almost trivial, to establish the lack of Doppler shift between emitter and absorber in the laboratory frame.

A reference frame in which the time coordinate defines proper time for all co- moving observers is called "synchronous". It is built by choosing some constant time hypersurface as an origin, such that has in every point a normal along the time line (lies inside the light cone with an apex in that point); all interval elements on this hypersurface are space-like. A family of geodesics normal to this hypersurface are drawn and defined as the time coordinates with a beginning at the hypersurface. Such a construct, and hence, choice of synchronous frame, is always possible though it is not unique.

Additional co-rotation torques are also exerted by gas orbiting with a period similar to that of the planet. In a reference frame attached to the planet, this gas follows horseshoe orbits, reversing direction when it approaches the planet from ahead or from behind. The gas reversing course ahead of the planet originates from a larger semi-major axis and may be cooler and denser than the gas reversing course behind the planet. This may result in a region of excess density ahead of the planet and of lesser density behind the planet, causing the planet to gain angular momentum.

The shape of this arc is reminiscent of a horseshoe, from which comes the name "horseshoe orbit". As it moves along the Earth's orbit, it winds in a spiral about it, in which each loop of the spiral takes one year. This spiral motion (in the Earth–Sun reference frame) arises from the slightly lower eccentricity and the tilt of the orbit: the inclination relative to the Earth's orbit is responsible for the vertical component of the spiral loop, and the difference in eccentricity for the horizontal component. When is approaching the Earth from in front (i.e.

The direct-quadrature-zero (DQZ or DQ0 or DQO, sometimes lowercase) transformation or zero-direct-quadrature (0DQ or ODQ, sometimes lowercase) transformation is a tensor that rotates the reference frame of a three-element vector or a three-by-three element matrix in an effort to simplify analysis. The DQZ transform is the product of the Clarke transform and the Park transform, first proposed in 1929 by Robert H. Park.R.H. Park Two Reaction Theory of Synchronous Machines AIEE Transactions 48:716–730 (1929). The DQZ transform is often used in the context of electrical engineering with three- phase circuits.

These changes are insignificant if a local datum is used, but are statistically significant if a global datum is used. Examples of global datums include World Geodetic System (WGS 84, also known as EPSG:4326 ), the default datum used for the Global Positioning System, and the International Terrestrial Reference Frame (ITRF), used for estimating continental drift and crustal deformation. The distance to Earth's center can be used both for very deep positions and for positions in space. Local datums chosen by a national cartographical organization include the North American Datum, the European ED50, and the British OSGB36.

The reference frame is relatively stationary, aligned with the vernal equinox. A rectangular variant of ecliptic coordinates is often used in orbital calculations and simulations. It has its origin at the center of the Sun (or at the barycenter of the Solar System), its fundamental plane on the ecliptic plane, and the -axis toward the vernal equinox. The coordinates have a right-handed convention, that is, if one extends their right thumb upward, it simulates the -axis, their extended index finger the -axis, and the curl of the other fingers points generally in the direction of the -axis.

Assuming that the electron and ion temperatures range from ~0.1 eV to 0.35 eV, the resulting ion velocity ranges from 875 m/s to 4.0 km/s from 200 km to 2000 km altitude, respectively. The electrons are traveling at approximately 188 km/s throughout LEO. This means that the orbiting body is traveling faster than the ions and slower than the electrons, or at a mesosonic speed. This results in a unique phenomenon whereby the orbiting body 'rams' through the surrounding ions in the plasma creating a beam like effect in the reference frame of the orbiting body.

The postulates of special relativity can be expressed very succinctly using the mathematical language of pseudo- Riemannian manifolds. The second postulate is then an assertion that the four- dimensional spacetime M is a pseudo-Riemannian manifold equipped with a metric g of signature (1,3), which is given by the Minkowski metric when measured in each inertial reference frame. This metric is viewed as one of the physical quantities of the theory; thus it transforms in a certain manner when the frame of reference is changed, and it can be legitimately used in describing the laws of physics.

The period of the Moon's orbit as defined with respect to the celestial sphere of apparently fixed stars (the International Celestial Reference Frame; ICRF) is known as a sidereal month because it is the time it takes the Moon to return to a similar position among the stars (): days (27 d 7 h 43 m 11.6 s). This type of month has been observed among cultures in the Middle East, India, and China in the following way: they divided the sky into 27 or 28 lunar mansions, one for each day of the month, identified by the prominent star(s) in them.

This latter frame is considered to be an inertial reference frame, although it too is non-inertial in more subtle ways. The Earth frame is well known to be non- inertial, a fact made perceivable by the apparent presence of centrifugal forces and Coriolis forces. Motion along the line of latitude is parameterized by the passage of time, and the Foucault pendulum's plane of oscillation appears to rotate about the local vertical axis as time passes. The angle of rotation of this plane at a time t with respect to the initial orientation is the anholonomy of the system.

Wardleworth was a township at the geographic centre of the Parish of Rochdale, in Salford Hundred, Lancashire, England.A vision of Butterworth Tn/CP The principal estate of the township was Buckley. Though the administrative territory has long been abolished, the name continues as a geographic reference frame for that part of Rochdale. Wardleworth was a township that included territory to the northeast of the town of Rochdale, including the hamlets of Buckley, Crankey Shaw and Hamer Fold, and, although close to the village of Wardle, Wardleworth did not contain the settlement, which was instead within the neighbouring township of Wuerdle and Wardle.

Finally, one may ask how an inertial frame can be found, and the answer lies in the Newton's laws, at least in Newtonian mechanics: the first law guarantees the existence of an inertial frame while the second and third law are used to examine whether a given reference frame is an inertial one or not. It may appear an inertial frame can now be easily found given the Newton's laws as empirical tests are accessible. Quite the contrary; an absolutely inertial frame is not and will most likely never be known. Instead, inertial frame is approximated.

Incl .. 24.66109 where the epoch is expressed in terms of Terrestrial Time, with an equivalent Julian date. Four of the elements are independent of any particular coordinate system: M is mean anomaly (deg), n: mean daily motion (deg/d), a: size of semi-major axis (AU), e: eccentricity (dimensionless). But the argument of perihelion, longitude of the ascending node and the inclination are all coordinate-dependent, and are specified relative to the reference frame of the equinox and ecliptic of another date "2000.0", otherwise known as J2000, i.e. January 1.5, 2000 (12h on January 1) or JD 2451545.0.

Inter- frame coding works by comparing each frame in the video with the previous one. Individual frames of a video sequence are compared from one frame to the next, and the video compression codec sends only the differences to the reference frame. If the frame contains areas where nothing has moved, the system can simply issue a short command that copies that part of the previous frame into the next one. If sections of the frame move in a simple manner, the compressor can emit a (slightly longer) command that tells the decompressor to shift, rotate, lighten, or darken the copy.

SLR data has provided the standard, highly accurate, long wavelength gravity field reference model which supports all precision orbit determination and provides the basis for studying temporal gravitational variations due to mass redistribution. The height of the geoid has been determined to less than ten centimeters at long wavelengths less than 1,500 km. SLR provides mm/year accurate determinations of tectonic drift station motion on a global scale in a geocentric reference frame. Combined with gravity models and decadal changes in Earth rotation, these results contribute to modeling of convection in the Earth’s mantle by providing constraints on related Earth interior processes.

Olya MO "Ola village council" in the future city of Olya. As part of the project is aimed at the port waters of port facilities with a total length of berths about 5 km, reservation areas for possible development in the area of industrial and commercial facilities and warehouses for transshipment and other goods. In addition, they plan to strengthen the role of the district center ( village Lyman) and the strengthening of the reference frame formed settlements on the basis of organizational and business functions support centers settlement systems. The future will remain 24 rural settlements, due to a small sseleniya (p.

The Earth constitutes a rotating reference frame because it rotates once every 23 hours and 56 minutes around its axis. Because the rotation is slow, the fictitious forces it produces are often small, and in everyday situations can generally be neglected. Even in calculations requiring high precision, the centrifugal force is generally not explicitly included, but rather lumped in with the gravitational force: the strength and direction of the local "gravity" at any point on the Earth's surface is actually a combination of gravitational and centrifugal forces. However, the fictitious forces can be of arbitrary size.

Macrossan (1986) Independently of Larmor, also Lorentz (1899) extended his transformation for second order terms and noted a (mathematical) time dilation effect as well. Other physicists besides Lorentz and Larmor also tried to develop a consistent model of electrodynamics. For example, Emil Cohn (1900, 1901) created an alternative electrodynamics in which he, as one of the first, discarded the existence of the aether (at least in the previous form) and would use, like Ernst Mach, the fixed stars as a reference frame instead. Due to inconsistencies within his theory, like different light speeds in different directions, it was superseded by Lorentz's and Einstein's.

The driver of the train sees the ball approaching at 80 km/h and then departing at 80 km/h after the ball bounces elastically off the front of the train. Because of the train's motion, however, that departure is at 130 km/h relative to the train platform; the ball has added twice the train's velocity to its own. Translating this analogy into space: in the planet reference frame, the spaceship has a vertical velocity of v relative to the planet. After the slingshot occurs the spaceship is leaving on a course 90 degrees to that which it arrived on.

It will still have a velocity of v, but in the horizontal direction. In the Sun reference frame, the planet has a horizontal velocity of v, and by using the Pythagorean Theorem, the spaceship initially has a total velocity of v. After the spaceship leaves the planet, it will have a velocity of v + v = 2v, gaining around 0.6v. This oversimplified example is impossible to refine without additional details regarding the orbit, but if the spaceship travels in a path which forms a hyperbola, it can leave the planet in the opposite direction without firing its engine.

P. Foley and D.A. Mindell, "Precision Survey and Archaeological Methodology in Deep Water," ENALIA The Journal of the Hellenic Institute of Marine Archaeology, Vol. VI, 49-56, 2002 This is due to the fact that the transponders are installed in the reference frame of the work site itself (i.e. on the sea floor), the wide transponder spacing results in an ideal geometry for position computations, and the LBL system operates without an acoustic path to the (potentially distant) sea surface. Ultra-short-baseline (USBL) systems and the related super-short-baseline (SSBL) systems rely on a small (ex.

Epimetheus (lower left) and Janus (right) seen on 20 March 2006, two months after swapping orbits. The two moons appear close only because of foreshortening; in reality, Janus is about 40,000 km farther from Cassini than Epimetheus. Rotating-frame depiction of the horseshoe orbits of Janus and Epimetheus Animation of Epimetheus orbit – Rotating reference frame Epimetheus's orbit is co-orbital with that of Janus. Janus's mean orbital radius from Saturn is, as of 2006 (as shown by green color in the adjacent picture), only 50 km less than that of Epimetheus, a distance smaller than either moon's mean radius.

If the object is less dense than the liquid, the force can keep the object afloat. This can occur only in a non-inertial reference frame, which either has a gravitational field or is accelerating due to a force other than gravity defining a "downward" direction.Note: In the absence of surface tension, the mass of fluid displaced is equal to the submerged volume multiplied by the fluid density. High repulsive surface tension will cause the body to float higher than expected, though the same total volume will be displaced, but at a greater distance from the object.

In the Solar System, a planet is said to be inferior or interior with respect to another planet if its orbit lies inside the other planet's orbit around the Sun. In this situation, the latter planet is said to be superior to the former. In the reference frame of the Earth, in which the terms were originally used, the inferior planets are Mercury and Venus, while the superior planets are Mars, Jupiter, Saturn, Uranus and Neptune. Dwarf planets like Ceres or Pluto and most asteroids are 'superior' in the sense that they almost all orbit outside the orbit of Earth.

The Alcubierre metric defines the warp-drive spacetime. It is a Lorentzian manifold that, if interpreted in the context of general relativity, allows a warp bubble to appear in previously flat spacetime and move away effectively faster than lightspeed. The interior of the bubble is an inertial reference frame and inhabitants experience no proper acceleration. This method of transport does not involve objects in motion at speeds faster than light with respect to the contents of the warp bubble; that is, a light beam within the warp bubble would still always move faster than the ship.

The satellite observations essentially yielded highly accurate relative positions of stars with respect to each other, throughout the measurement period (1989–93). In the absence of direct observations of extragalactic sources (apart from marginal observations of quasar 3C273) the resulting rigid reference frame was transformed to an inertial frame of reference linked to extragalactic sources. This allows surveys at different wavelengths to be directly correlated with the Hipparcos stars, and ensures that the catalogue proper motions are, as far as possible, kinematically non-rotating. The determination of the relevant three solid-body rotation angles, and the three time-dependent rotation rates, was conducted and completed in advance of the catalogue publication.

For example, they reflect the fact that observers moving at different velocities may measure different distances, elapsed times, and even different orderings of events, but always such that the speed of light is the same in all inertial reference frames. The invariance of light speed is one of the postulates of special relativity. Historically, the transformations were the result of attempts by Lorentz and others to explain how the speed of light was observed to be independent of the reference frame, and to understand the symmetries of the laws of electromagnetism. The Lorentz transformation is in accordance with Albert Einstein's special relativity, but was derived first.

This effect causes the distant fields of unaccelerated moving charges to appear to be "updated" instantly for their constant velocity motion, as seen from distant positions, in the frame where the source-object is moving at constant velocity. However, as discussed, this is an effect which can be removed at any time, by transitioning to a new reference frame in which the distant charged body is now at rest. The static and continuous gravitoelectric component of a gravitational field is not a gravitomagnetic component (gravitational radiation); see Petrov classification. The gravitoelectric field is a static field and therefore cannot superluminally transmit quantized (discrete) information, i.e.

In 1990, the Orbital Mechanics Department and Astronomical Applications Department were established, and Nautical Almanac Office became a division of the Astronomical Applications Department. The Orbital Mechanics Department operated under P. K. Seidelmann until 1994 when the department was abolished, and its functions were moved to a group within the Astronomical Applications Department. In 2010, USNO's astronomical 'department' known as the Naval Observatory Flagstaff Station (NOFS) was officially made autonomous as an Echelon Five command separate from USNO, but reporting to it. In the alpine woodlands above 7,000 feet altitude outside Flagstaff, Arizona, NOFS performs its national, Celestial Reference Frame (CRF) mission under dark skies in that region.

In both cases, during the interval energy will not be conserved. A stronger form of conservation law requires that, for the amount of a conserved quantity at a point to change, there must be a flow, or flux of the quantity into or out of the point. For example, the amount of electric charge at a point is never found to change without an electric current into or out of the point that carries the difference in charge. Since it only involves continuous local changes, this stronger type of conservation law is Lorentz invariant; a quantity conserved in one reference frame is conserved in all moving reference frames.

The J2000.0 epoch is precisely Julian date 2451545.0 TT (Terrestrial Time), or January 1, 2000, noon TT. This is equivalent to January 1, 2000, 11:59:27.816 TAI or January 1, 2000, 11:58:55.816 UTC. Since the right ascension and declination of stars are constantly changing due to precession, (and, for relatively nearby stars due to proper motion), astronomers always specify these with reference to a particular epoch. The earlier epoch that was in standard use was the B1950.0 epoch. When the mean equator and equinox of J2000 are used to define a celestial reference frame, that frame may also be denoted J2000 coordinates or simply J2000.

The hadron is defined in a reference frame where it has infinite momentum—a valid approximation at high energies. Thus, parton motion is slowed by time dilation, and the hadron charge distribution is Lorentz- contracted, so incoming particles will be scattered "instantaneously and incoherently". Partons are defined with respect to a physical scale (as probed by the inverse of the momentum transfer). For instance, a quark parton at one length scale can turn out to be a superposition of a quark parton state with a quark parton and a gluon parton state together with other states with more partons at a smaller length scale.

Extract of page 272 The principle requires physical laws to be the same for any body moving at constant velocity as they are for a body at rest. A consequence is that an observer in an inertial reference frame cannot determine an absolute speed or direction of travel in space, and may only speak of speed or direction relative to some other object. The principle does not extend to non-inertial reference frames because those frames do not, in general experience, seem to abide by the same laws of physics. In classical physics, fictitious forces are used to describe acceleration in non-inertial reference frames.

Geological structures can be mapped by observing how they affect seismic waves from local and distant earthquakes, a process known as seismic tomography. The density of the TA network — typical station spacing of about 70 km — provides a level of resolution not previously available in many parts of the country, and is providing finer details of the lithosphere under parts of North America. The Reference Network is an additional 100+ permanent stations located on approximately 300 km spacings that provide a long-term reference frame. These also augment the USGS Advanced National Seismic System (ANSS), providing seismic observations in areas where instrumentation has been lacking.

This is an apparent, but fictitious, force that arises when an observer is in a rotating reference frame, due to the conservation of angular momentum of the air as it moves towards or away from the Earth's axis of rotation. Viewed from above this twist in wind direction is in the opposite direction as the rotation of the planet. The strongest high-pressure areas are associated with cold air masses which push away out of polar regions during the winter when there is less sun to warm neighboring regions. These Highs change character and weaken once they move further over relatively warmer water bodies.

The transform can be used to rotate the reference frames of ac waveforms such that they become dc signals. Simplified calculations can then be carried out on these dc quantities before performing the inverse transform to recover the actual three-phase ac results. As an example, the DQZ transform is often used in order to simplify the analysis of three-phase synchronous machines or to simplify calculations for the control of three-phase inverters. In analysis of three-phase synchronous machines the transformation transfers three-phase stator and rotor quantities into a single rotating reference frame to eliminate the effect of time-varying inductances.

In electric systems, very often the A, B, and C values are oscillating in such a way that the net vector is spinning. In a balanced system, the vector is spinning about the Z axis. Very often, it is helpful to rotate the reference frame such that the majority of the changes in the abc values, due to this spinning, are canceled out and any finer variations become more obvious. The DQZ transformation can be thought of in geometric terms as the projection of the three separate sinusoidal phase quantities onto two axes rotating with the same angular velocity as the sinusoidal phase quantities.

Enterprise architecture (EA) presents a high level design of enterprise capabilities that defines successful IT projects in coherence with enterprise principals and business related requirements. EA covers mainly (i) the business capabilities analysis and validation; (ii) the development of business, application, data and technical architectures and solutions, and finally (iii) the control of programme and project implementation and governance. The application of EA methodology feeds the enterprise repository reference frame with sets of building blocks used to compose the targeted system. The interoperability can be considered either as a principal, requirement or constraint that impact the definition of patterns to compose building blocks in the definition of targeted architectural roadmap.

When the conducting body is negatively biased with respect to the plasma and traveling above the ion thermal velocity, there are additional collection mechanisms at work. For typical Low Earth Orbits (LEOs), between 200 km and 2000 km,Gregory, F. D., "NASA Safety Standard Guidelines and Assessment Procedures for Limiting Orbital Debris," NASA, NSS 1740.14, Washington D.C., 1995 the velocities in an inertial reference frame range from 7.8 km/s to 6.9 km/s for a circular orbit and the atmospheric molecular weights range from 25.0 amu (O+, O2+, & NO+) to 1.2 amu (mostly H+), respectively.Bilitza, D., "International Reference Ionosphere 2000," Radio Science, Vol. 36, No. 2, 2001, pp. 261–275.

In one form, the navigational system of equations acquires linear and angular measurements from the inertial and body frame, respectively and calculates the final attitude and position in the NED frame of reference. 600px Where: f is specific force, \omega is angular rate, a is acceleration, R is position, \dot R and V are velocity, \Omega is the angular velocity of the earth, g is the acceleration due to gravity, \Phi, \lambda and h are the NED location parameters. Also, super/subscripts of E, I and B are representing variables in the Earth centered, Inertial or Body reference frame, respectively and C is a transformation of reference frames.

This historic moment was of little interest to the crew, since they were still calculating their trajectory with respect to the launch pad at Kennedy Space Center. They would continue to do so until they performed their last mid- course correction, switching to a reference frame based on ideal orientation for the second engine burn they would make in lunar orbit. The last major event before Lunar Orbit Insertion (LOI) was a second mid-course correction. It was in retrograde (against the direction of travel) and slowed the spacecraft down by , effectively reducing the closest distance at which the spacecraft would pass the Moon.

The rigid rotating disk had been a topic of lively discussion since Max Born and Paul Ehrenfest, in 1909, both presented analyses of rigid bodies in special relativity. An observer on the edge of a rotating disk experiences an apparent ("fictitious" or "pseudo") force called "centrifugal force". By 1912, Einstein had become convinced of a close relationship between gravitation and pseudo- forces such as centrifugal force: In the accompanying illustration, A represents a circular disk of 10 units diameter at rest in an inertial reference frame. The circumference of the disk is \pi times the diameter, and the illustration shows 31.4 rulers laid out along the circumference.

As long as the error of the approximation is undetectable by measurements, the approximately inertial frame (or simply "effective frame") is reasonably close to an absolutely inertial frame. With the effective frame and assuming the physical laws are valid in such frame, descriptions of systems will ends up as good as if the absolutely inertial frame was used. As a digression, the effective frame Astronomers use is a system called "International Celestial Reference Frame" (ICRF), defined by 212 radio sources and with an accuracy of about 10^{-5} radians. However, it is likely that a better one will be needed when a more accurate approximation is required.

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 Newton's time the fixed stars were invoked as a reference frame supposedly at rest relative to absolute space. In other reference frames either at rest with respect to the fixed stars or in uniform translation relative to these stars, Newton's laws of motion were supposed to hold. In contrast, in frames accelerating with respect to the fixed stars, in particular frames rotating relative to the fixed stars, the laws of motion did not hold in their simplest form, but had to be supplemented by the addition of fictitious forces, for example, the Coriolis force and the centrifugal force. As we now know, the fixed stars are not fixed.

Human bodily experience is characterized by the immediate and continuous experience that our body and its parts belong to us, often called self-attribution, body ownership and or mineness. It is unknown if the origin of body representation is innate or if it is constructed from sensory experience.Marcello Costantini, Patrick Haggard, "The rubber hand illusion: Sensitivity and reference frame for body ownership", Consciousness and Cognition, Volume 16, Issue 2, June 2007, Pages 229–240, ISSN 1053-8100, . A related, but distinct, bodily experience is self-localization or embodiment that is defined as the experience that the self is localized at the position of our body at a certain position in space.

Rotation, precession, and nutation in obliquity of a planet Nutation (from Latin nūtātiō, "nodding, swaying") is a rocking, swaying, or nodding motion in the axis of rotation of a largely axially symmetric object, such as a gyroscope, planet, or bullet in flight, or as an intended behaviour of a mechanism. In an appropriate reference frame it can be defined as a change in the second Euler angle. If it is not caused by forces external to the body, it is called free nutation or Euler nutation. A pure nutation is a movement of a rotational axis such that the first Euler angle is constant.

This approach places more emphasis on the many choices for description open to an observer. The observer is then identified with an observational reference frame, rather than with the combination of coordinate system, measurement apparatus and state of motion. It also has been suggested that the term "observer" is antiquated, and should be replaced by an observer team (or family of observers) in which each observer makes observations in their immediate vicinity, where delays are negligible, cooperating with the rest of the team to set up synchronized clocks across the entire region of observation, and all team members sending their various results back to a data collector for synthesis.

In all inertial reference frames, while weightlessness is experienced, Newton's first law of motion is obeyed locally within the frame. Inside the frame (for example, inside an orbiting ship or free-falling elevator), unforced objects keep their velocity relative to the frame. Objects not in contact with other objects "float" freely. If the inertial trajectory is influenced by gravity, the reference frame will be an accelerated frame as seen from a position outside the gravitational attraction, and (seen from far away) the objects in the frame (elevator, etc.) will appear to be under the influence of a force (the so-called force of gravity).

A scalar field such as temperature or pressure, where intensity of the field is represented by different hues of colors. In mathematics and physics, a scalar field associates a scalar value to every point in a space – possibly physical space. The scalar may either be a (dimensionless) mathematical number or a physical quantity. In a physical context, scalar fields are required to be independent of the choice of reference frame, meaning that any two observers using the same units will agree on the value of the scalar field at the same absolute point in space (or spacetime) regardless of their respective points of origin.

Einstein (The Meaning of Relativity): "Two events taking place at the points A and B of a system K are simultaneous if they appear at the same instant when observed from the middle point, M, of the interval AB. Time is then defined as the ensemble of the indications of similar clocks, at rest relative to K, which register the same simultaneously." Einstein wrote in his book, Relativity, that simultaneity is also relative, i.e., two events that appear simultaneous to an observer in a particular inertial reference frame need not be judged as simultaneous by a second observer in a different inertial frame of reference.

Yuca Vitín and Indio Nando had a rather constant routine: they opened telephone lines to ask listeners to suggest a public Puerto Rican personality annoying enough to be either scalped or flogged. Since their time reference frame was 1493 (the year when Puerto Rico was "discovered" by Christopher Columbus' naval crews), they answered "the spirits talking over the magic stone" (i.e. the voice at the speaker phone) very reverently. Once the audience agreed on a candidate, Yuca Vitín and Indio Nando would simulate a hunt for the character, complete with jungle sound effects, a verbal description of the celebrity using archaic language references (i.e.

This is a result of the Earth turning 1 additional rotation, relative to the celestial reference frame, as it orbits the Sun (so 366.25 rotations/y). The mean solar day in SI seconds is available from the IERS for the periods IERS Excess of the duration of the day to 86,400s … since 1623 Graph at end. and . Recently (1999–2010) the average annual length of the mean solar day in excess of has varied between and , which must be added to both the stellar and sidereal days given in mean solar time above to obtain their lengths in SI seconds (see Fluctuations in the length of day).

Guillaume Aigoin, Characterising hard landings / EASA EOFDM Conference, 12 January 2012, page 7: "The vertical parameter is neither vertical nor an acceleration … It is the normal load factor in the aircraft reference frame is not sufficient for assessing contact severity!" Hard landings can be caused by weather conditions, mechanical problems, over-weight aircraft, pilot decision and/or pilot error. The term hard landing usually implies that the pilot still has total or partial control over the aircraft, as opposed to an uncontrolled descent into terrain (a crash). Hard landings can vary in their consequences, from mild passenger discomfort to vehicle damage, structural failure, injuries, and/or loss of life.

This relativity of simultaneity means that switching from one inertial frame to another requires an adjustment in what slice through spacetime counts as the "present". In the spacetime diagram on the right, drawn for the reference frame of the Earth-based twin, that twin's world line coincides with the vertical axis (his position is constant in space, moving only in time). On the first leg of the trip, the second twin moves to the right (black sloped line); and on the second leg, back to the left. Blue lines show the planes of simultaneity for the traveling twin during the first leg of the journey; red lines, during the second leg.

A perturbation of nuclear spin orientations from equilibrium will occur only when an oscillating magnetic field is applied whose frequency νrf sufficiently closely matches the Larmor precession frequency νL of the nuclear magnetization. The populations of the spin-up and -down energy levels then undergo Rabi oscillations, which are analyzed most easily in terms of precession of the spin magnetization around the effective magnetic field in a reference frame rotating with the frequency νrf.A. Abragam, The Principles of Nuclear Magnetism, Ch. 2, Oxford Clarendon Press, 1961. The stronger the oscillating field, the faster the Rabi oscillations or the precession around the effective field in the rotating frame.

Multiple reference frames can considerably increase encoding time because many of the decisions, such as motion estimation, that are ordinarily carried out only on one reference frame have to be repeated on all of the reference frames. Heuristics can be used to reduce this speed cost at the cost of quality. Very high numbers of reference frames are rarely useful in terms of quality for live-action material because frames from farther back in time generally have less and less correlation with the current frame. This is not as true for animated sources, where repetitive motion can make high numbers of reference frames more useful.

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.

To improve the National Spatial Reference System (NSRS), the National Geodetic Service will replace the North American Datum of 1983 (NAD 83) and the North American Vertical Datum of 1988 (NAVD 88) with a new geometric reference frame and geopotential datum in 2022. The new reference frames will rely primarily on Global Navigation Satellite Systems (GNSS), such as the Global Positioning System (GPS), as well as on a gravimetric geoid model resulting from NOAA's Gravity for the Redefinition of the American Vertical Datum (GRAV-D) Project. These new reference frames are intended be easier to access and to maintain than NAD 83 and NAVD 88, which rely on physical survey marks that deteriorate over time.

In 1917, as a wartime measure to improve efficiency, the districts were further subdivided with a number applied to each sub-district. This was achieved by designating a sub-area served most conveniently by the head office in each district "1" and then allocating the rest alphabetically by the name of the location of each delivery office. Exceptionally, W2 and SW11 are also 'head districts'. The boundaries of each sub-district rarely correspond to any units of civil administration: the parishes and hamlets/chapelries with chapels that traditionally define settlement names everywhere in England and Wales or the generally larger boroughs; despite this, postal sub-districts have developed over time into a primary reference frame.

The Ehlers–Geren–Sachs theorem, published in 1968 by Jürgen Ehlers, P. Geren and R. Sachs, shows that if, in a given universe, there exists a reference frame at each event such that the cosmic background radiation is isotropic, then under certain conditions that universe is an isotropic and homogeneous FLRW spacetime. From 1969 to 1993, he was Professor of Math and Physics at the University of California, Berkeley (UCB), and from 1993 he has been Professor Emeritus at UCB. In 1994, he was appointed Research Professor of Mathematics UCB, and since 2005 he has been an Adjunct Professor at the Tufts medical school. Until 1985, he worked on general relativistic cosmology and astrophysics.

Thus, time runs more slowly for observers who are lower in a gravitational field. It is important to stress that, for each observer, there are no observable changes of the flow of time for events or processes that are at rest in his or her reference frame. Five-minute-eggs as timed by each observer's clock have the same consistency; as one year passes on each clock, each observer ages by that amount; each clock, in short, is in perfect agreement with all processes happening in its immediate vicinity. It is only when the clocks are compared between separate observers that one can notice that time runs more slowly for the lower observer than for the higher.

To improve the National Spatial Reference System NAD 83, along with North American Vertical Datum of 1988 (NAVD 88), is set to be replaced with a new GNSS- and gravimetric geoid model-based geometric reference frame and geopotential datum in 2022. The new reference frames will rely primarily on Global Navigation Satellite Systems (GNSS), such as the Global Positioning System (GPS), as well as on a gravimetric geoid model resulting from our Gravity for the Redefinition of the American Vertical Datum (GRAV-D) Project. These new reference frames are intended to be easier to access and to maintain than NAD 83 and NAVD 88, which rely on physical survey marks that deteriorate over time.

In 1971, with funding by the Government of Western Australia and negotiations for the loan of the Hamburg telescope, Nikoloff was placed in charge of the newly formed Perth Observatory Meridian Section. Dr Nikoloff commenced a new observing program of FK4 and FK4 Supplementary stars that would result in the Perth 75 catalogue of 2549 stars. The catalogue not only extended the well revered Perth 70 catalogue, but provided valuable Southern Hemisphere information for the construction of the new FK5 reference frame sought by the international astronomical community. As Government Astronomer, Nikoloff passed on the Meridian Section to D. Harwood, but kept a keen involvement in the construction of the subsequent Perth 83 meridian catalogue.

Poles from different ages in a single continent, lithospheric plate, or any other tectonic block can be used to construct an apparent polar wander path (APWP). If paths from adjacent crustal fragments are identical, this is taken to indicate that there has been no relative movement between them during the period covered by the path. Divergence of APW paths indicates that the areas in question have acted independently in the past with the point of divergence marking the time at which they became joined. Combined or synthetic APWPs can be constructed by rotating paleomagnetic poles from different plates into the reference frame fixed to a single plate, using estimates of relative plate motions.

Since the local government reforms of 1974, some of the people of Saddleworth have been uneasy about their primary geographic reference frame, with parts of the local community feeling aggrieved at Saddleworth forming part of Greater Manchester. Saddleworth, where the local architecture of stone cottages is of the Yorkshire type, is the only part of the Metropolitan Borough of Oldham to come from the historic county boundaries of Yorkshire, the rest being from Lancashire. It is also the only part of the metropolitan county of Greater Manchester which lay within those borders. Greater Manchester is based on the conurbation of towns surrounding the city of Manchester with relatively few villages in between.

The data base of the cities, the data base of leveling distribution, the data base of geodesic distribution, the aerial missions data base and the toponyms data base were progressively established . The "Topo data base", bases of topographic data digitized, covers from now on the whole of France and includes nearly two million toponyms. Its activities abroad begin into 1986 within a new subsidiary private company IGN France International. From 2000, the IGN develops the concept of Reference frame on a Large Scale (référentiel à grande échelle = RGE); it is a question of completing within a deadline short digitalization the cartography of the French territory with a meter scale and according to four components: topography, land registry and address.

EUREF is driven by a voluntary agreement of scientific organisations and national geodetic/geographic agencies of the member countries, who are willing to replace their legacy national geodetic datums with a unified European Reference Frame and join their national networks of reference stations into a common European network. The mandate of EUREF is to foster and coordinate the activities of the member countries, which are financed and managed on the national level. EUREF realizes and maintains ETRS89, the European geodetic datum, which is to become a single datum used for geodetic applications in all the member countries. A key instrument in maintaining ETRS89 is the EUREF Permanent Network (EPN), a network of reference stations which covers the European continent.

Different astronomers or groups of astronomers used to define individually, but today standard epochs are generally defined by international agreement through the IAU, so astronomers worldwide can collaborate more effectively. It is inefficient and error-prone if data or observations of one group have to be translated in non- standard ways so that other groups could compare the data with information from other sources. An example of how this works: if a star's position is measured by someone today, they then use a standard transformation to obtain the position expressed in terms of the standard reference frame of J2000, and it is often then this J2000 position which is shared with others.

Analysis and observation of circular motion in the rotating frame is a simplification compared with analysis and observation of elliptical motion in the inertial frame. Because this reference frame rotates several times a minute rather than only once a day like the Earth, the Coriolis acceleration produced is many times larger and so easier to observe on small time and spatial scales than is the Coriolis acceleration caused by the rotation of the Earth. In a manner of speaking, the Earth is analogous to such a turntable. The rotation has caused the planet to settle on a spheroid shape, such that the normal force, the gravitational force and the centrifugal force exactly balance each other on a "horizontal" surface.

In the inertial frame of reference (upper part of the picture), the black ball moves in a straight line. However, the observer (red dot) who is standing in the rotating/non-inertial frame of reference (lower part of the picture) sees the object as following a curved path due to the Coriolis and centrifugal forces present in this frame. In physics, the Coriolis force is an inertial or fictitious force Extract of page 208 that acts on objects that are in motion within a frame of reference that rotates with respect to an inertial frame. In a reference frame with clockwise rotation, the force acts to the left of the motion of the object.

Another common approach is to dislodge the starch grains through sonication, which is a laboratory technique that uses sound waves to "agitate particles" in order to convert an electrical signal into a vibration which in turn breaks down a substance. In terms of starch grain analysis, the starch grains are released by use of an ultrasonic bath and the distilled water containing the sample particles is then centrifuged. This is the process in which the specimens are spun and separated by density as a result of centripetal force, or due to the fictitious centrifugal force that is felt by the specimens due to their reference frame. Utilizing this force allows for the separation of solutions of different densities.

His reasoning was the same as Bradley's, but it required that this medium be immobile in the Sun's reference frame and must pass through the earth unaffected, otherwise the medium (and therefore the light) would move along with the earth and no aberration would be observed. He wrote: However, it soon became clear Young's theory could not account for aberration when materials with a non-vacuum index of refraction were present. An important example is of a telescope filled with water. The velocity of the light in such a telescope will be slower than in vacuum, and is given by c/n rather than c where n is the index of refraction of the water.

Reference frames are inherently nonlocal constructs, covering all of space and time or a nontrivial part of it; thus it does not make sense to speak of an observer (in the special relativistic sense) having a location. Also, an inertial observer cannot accelerate at a later time, nor can an accelerating observer stop accelerating. Physicists use the term "observer" as shorthand for a specific reference frame from which a set of objects or events is being measured. Speaking of an observer in special relativity is not specifically hypothesizing an individual person who is experiencing events, but rather it is a particular mathematical context which objects and events are to be evaluated from.

Einstein (1907) He wrote in 1920: Minkowski argued that Lorentz's introduction of the contraction hypothesis "sounds rather fantastical", since it is not the product of resistance in the aether but a "gift from above". He said that this hypothesis is "completely equivalent with the new concept of space and time", though it becomes much more comprehensible in the framework of the new spacetime geometry.Minkowski (1908) However, Lorentz disagreed that it was "ad-hoc" and he argued in 1913 that there is little difference between his theory and the negation of a preferred reference frame, as in the theory of Einstein and Minkowski, so that it is a matter of taste which theory one prefers.

At this speed, if a photon were travelling with the particle, it would take over 215,000 years for the photon to gain a 1 cm lead as seen from the Earth's reference frame. The energy of this particle is some 40 million times that of the highest energy protons that have been produced in any terrestrial particle accelerator. However, only a small fraction of this energy would be available for an interaction with a proton or neutron on Earth, with most of the energy remaining in the form of kinetic energy of the products of the interaction. The effective energy available for such a collision is , where is the particle's energy and is the mass energy of the proton.

Thus, this definition may be rephrased to say that a cylinder is any ruled surface spanned by a one-parameter family of parallel lines. A cylinder having a right section that is an ellipse, parabola, or hyperbola is called an elliptic cylinder, parabolic cylinder and hyperbolic cylinder, respectively. These are degenerate quadric surfaces. Parabolic cylinder When the principal axes of a quadric are aligned with the reference frame (always possible for a quadric), a general equation of the quadric in three dimensions is given by :f(x,y,z)=Ax^2 + By^2 + Cz^2 + Dx + Ey + Gz + H = 0, with the coefficients being real numbers and not all of , and being 0.

Elements by Simon Newcomb The low eccentricity and comparatively small size of its orbit give Venus the least range in distance between perihelion and aphelion of the planets: 1.46 Gm. The planet orbits the Sun once every 225 daysThe sidereal and anomalistic years are both 224.7008 days long. The sidereal year is the time taken to revolve around the Sun relative to a fixed reference frame. More precisely, the sidereal year is one way to express the rate of change of the mean longitude at one instant, with respect to a fixed equinox. The calculation shows how long it would take for the longitude to make one revolution at the given rate.

Because of this, energy release behind the shock is able to be transported acoustically to the shock for its support. For a self-propagating detonation, the shock relaxes to a speed given by the Chapman–Jouguet condition, which induces the material at the end of the reaction zone to have a locally sonic speed in the reference frame in which the shock is stationary. In effect, all of the chemical energy is harnessed to propagate the shock wave forward. However, in the 1960s, experiments revealed that gas-phase detonations were most often characterized by unsteady, three- dimensional structures, which can only in an averaged sense be predicted by one-dimensional steady theories.

Absolute scales are used when precise values are needed in comparison to a natural, unchanging zero point. Measurements of length, area and volume are inherently absolute, although measurements of distance are often based on an arbitrary starting point. Measurements of weight can be absolute, such as atomic weight, but more often they are measurements of the relationship between two masses, while measurements of speed are relative to an arbitrary reference frame. (Unlike many other measurements without a known, absolute minimum, speed has a known maximum and can be measured from a purely relative scale.) Absolute scales can be used for measuring a variety of things, from the flatness of an optical flat to neuroscientific tests.

While most of the energy released during gravitational collapse is emitted very quickly, an outside observer does not actually see the end of this process. Even though the collapse takes a finite amount of time from the reference frame of infalling matter, a distant observer would see the infalling material slow and halt just above the event horizon, due to gravitational time dilation. Light from the collapsing material takes longer and longer to reach the observer, with the light emitted just before the event horizon forms delayed an infinite amount of time. Thus the external observer never sees the formation of the event horizon; instead, the collapsing material seems to become dimmer and increasingly red-shifted, eventually fading away.

The idea of the pseudo- Riemannian metric as a Higgs field appeared while constructing non-linear (induced) representations of the general linear group , of which the Lorentz group is a Cartan subgroup.M. Leclerc, "The Higgs sector of gravitational gauge theories", Annals of Physics 321 (2006) 708. The geometric equivalence principle postulating the existence of a reference frame in which Lorentz invariants are defined on the whole world manifold is the theoretical justification for the reduction of the structure group of the linear frame bundle to the Lorentz group. Then the very definition of a pseudo-Riemannian metric on a manifold X as a global section of the quotient bundle leads to its physical interpretation as a Higgs field.

In his Philosophiae Naturalis Principia Mathematica, he derived Kepler's laws from first principles. Those first principles are as follows: #In an inertial frame of reference, an object either remains at rest or continues to move at constant velocity, unless acted upon by a force. #In an inertial reference frame, the vector sum of the forces F on an object is equal to the mass m of that object multiplied by the acceleration a of the object: F = ma. (It is assumed here that the mass m is constant) #When one body exerts a force on a second body, the second body simultaneously exerts a force equal in magnitude and opposite in direction on the first body.

According to the first postulate of special relativity, all physical laws take their simplest form in an inertial frame, and there exist multiple inertial frames interrelated by uniform translation: This simplicity manifests in that inertial frames have self-contained physics without the need for external causes, while physics in non-inertial frames have external causes. The principle of simplicity can be used within Newtonian physics as well as in special relativity; see Nagel and also Blagojević. In practical terms, the equivalence of inertial reference frames means that scientists within a box moving uniformly cannot determine their absolute velocity by any experiment. Otherwise, the differences would set up an absolute standard reference frame.

The presence of fictitious forces indicates the physical laws are not the simplest laws available so, in terms of the special principle of relativity, a frame where fictitious forces are present is not an inertial frame: Bodies in non- inertial reference frames are subject to so-called fictitious forces (pseudo- forces); that is, forces that result from the acceleration of the reference frame itself and not from any physical force acting on the body. Examples of fictitious forces are the centrifugal force and the Coriolis force in rotating reference frames. How then, are "fictitious" forces to be separated from "real" forces? It is hard to apply the Newtonian definition of an inertial frame without this separation.

Thus the circle was aligned with the local vertical or plumb line, which is deflected slightly from the normal, or line perpendicular, to the reference ellipsoid used to define geodetic latitude and longitude in the International Terrestrial Reference Frame (which is nearly the same as the WGS-84 system used by GPS). While the local vertical defined at the Airy transit circle still points to the modern celestial meridian (the intersection of the prime meridian plane with the celestial sphere), it does not pass through the Earth's rotation axis. As a result of this, the ITRF zero meridian, defined by a plane passing through the Earth's rotation axis, is 102.478 metres to the east of the prime meridian. A 2015 analysis by Malys et al.

With the discovery of special relativity by Henri Poincaré and Albert Einstein, energy was proposed to be one component of an energy-momentum 4-vector. Each of the four components (one of energy and three of momentum) of this vector is separately conserved across time, in any closed system, as seen from any given inertial reference frame. Also conserved is the vector length (Minkowski norm), which is the rest mass for single particles, and the invariant mass for systems of particles (where momenta and energy are separately summed before the length is calculated—see the article on invariant mass). The relativistic energy of a single massive particle contains a term related to its rest mass in addition to its kinetic energy of motion.

In physics, the mathematical description of any physical situation usually contains excess degrees of freedom; the same physical situation is equally well described by many equivalent mathematical configurations. For instance, in Newtonian dynamics, if two configurations are related by a Galilean transformation (an inertial change of reference frame) they represent the same physical situation. These transformations form a group of "symmetries" of the theory, and a physical situation corresponds not to an individual mathematical configuration but to a class of configurations related to one another by this symmetry group. This idea can be generalized to include local as well as global symmetries, analogous to much more abstract "changes of coordinates" in a situation where there is no preferred "inertial" coordinate system that covers the entire physical system.

At the time of discovery, the asteroid orbited the Sun with a period of 365.389 days, close to Earth's 365.256 days. As long as it remains in 1:1 resonance with Earth, its average period over long time intervals will exactly equal that of Earth. On its eccentric (e = 0.191) orbit, 's distance from the Sun varies annually from 0.81 AU to 1.19 AU. It orbits in a plane inclined about 21 degrees to the plane of the ecliptic. Trojans do not orbit right at Lagrangian points but oscillate in tadpole-shaped loops around them (as viewed in a corotating reference frame in which the planet and Lagrangian points are stationary); traverses its loop over a period of 395 years.

The movement of components of a mechanical system are analyzed by attaching a reference frame to each part and determining how the various reference frames move relative to each other. If the structural stiffness of the parts are sufficient, then their deformation can be neglected and rigid transformations can be used to define this relative movement. This reduces the description of the motion of the various parts of a complicated mechanical system to a problem of describing the geometry of each part and geometric association of each part relative to other parts. Geometry is the study of the properties of figures that remain the same while the space is transformed in various ways—more technically, it is the study of invariants under a set of transformations.

Perhaps the most commonly encountered rotating reference frame is the Earth. Moving objects on the surface of the Earth experience a Coriolis force, and appear to veer to the right in the northern hemisphere, and to the left in the southern. Movements of air in the atmosphere and water in the ocean are notable examples of this behavior: rather than flowing directly from areas of high pressure to low pressure, as they would on a non-rotating planet, winds and currents tend to flow to the right of this direction north of the equator, and to the left of this direction south of the equator. This effect is responsible for the rotation of large cyclones (see Coriolis effects in meteorology).

Grøn states that the resolution of the paradox stems from the impossibility of synchronizing clocks in a rotating reference frame. If observers on the rotating circumference try to synchronise their clocks around the circumference to establish disc time, there is a time difference between the two end points where they meet. The modern resolution can be briefly summarized as follows: #Small distances measured by disk-riding observers are described by the Langevin–Landau–Lifschitz metric, which is indeed well approximated (for small angular velocity) by the geometry of the hyperbolic plane, just as Kaluza had claimed. #For physically reasonable materials, during the spin-up phase a real disk expands radially due to centrifugal forces; relativistic corrections partially counteract (but do not cancel) this Newtonian effect.

Pallas has a high eccentricity and a highly inclined orbit Pallas has unusual dynamic parameters for such a large body. Its orbit is highly inclined and moderately eccentric, despite being at the same distance from the Sun as the central part of the asteroid belt. Furthermore, Pallas has a very high axial tilt of 84°, with its north pole pointing towards ecliptic coordinates (β, λ) = (30°, −16°) with a 5° uncertainty in the Ecliptic J2000.0 reference frame. This means that every Palladian summer and winter, large parts of the surface are in constant sunlight or constant darkness for a time on the order of an Earth year, with areas near the poles experiencing continuous sunlight for as long as two years.

Relativistic Doppler shift for the longitudinal case, with source and receiver moving directly towards or away from each other, is often derived as if it were the classical phenomenon, but modified by the addition of a time dilation term. This is the approach employed in first-year physics or mechanics textbooks such as those by Feynman or Morin. Following this approach towards deriving the relativistic longitudinal Doppler effect, assume the receiver and the source are moving away from each other with a relative speed v\, as measured by an observer on the receiver or the source (The sign convention adopted here is that v\, is negative if the receiver and the source are moving towards each other). Consider the problem in the reference frame of the source.

In addition, a larger set of roughly six thousand secondary trig points were added to allow the construction of a finer mesh that extended the reference frame of the primary mesh over shorter distances. The calculations were constrained; it was hoped to minimise the shifts from the coordinates based on the old triangulation. At eleven primary trig points from Dunnose on the Isle of Wight (456784 m E, 080150 m N) north to Great Whernside in Yorkshire (400202 E, 473904 N) the new latitudes and longitudes were adjusted to stay within a metre of the old ones. Once the new latitude and longitude of those eleven points were fixed the calculated location of every other point in the triangulation was based on them.

The Unruh effect (or sometimes Fulling–Davies–Unruh effect) is the prediction that an accelerating observer will observe a thermal bath, like blackbody radiation, whereas an inertial observer would observe none. In other words, the background appears to be warm from an accelerating reference frame; in layman's terms, an accelerating thermometer (like one being waved around) in empty space, subtracting any other contribution to its temperature, will record a non-zero temperature, just from its acceleration. Heuristically, for a uniformly accelerating observer, the ground state of an inertial observer is seen as a mixed state in thermodynamic equilibrium with a non-zero temperature bath. The Unruh effect was first described by Stephen Fulling in 1973, Paul Davies in 1975 and W. G. Unruh in 1976.

This unexpected mass explains neutrinos with right-handed helicity and antineutrinos with left-handed helicity: Since they do not move at the speed of light, their helicity is not relativistic invariant (it is possible to move faster than them and observe the opposite helicity). Yet all neutrinos have been observed with left-handed chirality, and all antineutrinos right-handed. Chirality is a fundamental property of particles and is relativisticly invariant: It is the same regardless of the particle's speed and mass in every inertial reference frame. However, a particle with mass that starts out with left-handed chirality can develop a right-handed component as it travels – unless it is massless, chirality is not conserved during the propagation of a free particle through space.

For George Stokes (1845) the model of an aether which is totally unaffected or only partially affected by moving matter was unnatural and unconvincing, so he assumed that the aether is completely dragged within and in the vicinity of matter, partially dragged at larger distances, and stays at rest in free space. Also Heinrich Rudolf Hertz (1890) incorporated a complete aether drag model within his elaboration of Maxwell's theory of electromagnetism, to bring it into accord with the Galilean principle of relativity. That is, if it is assumed that the aether is at rest within matter in one reference frame, the Galilean transformation gives the result that matter and (entrained) aether travel with the same speed in another frame of reference.

For a video of the Coriolis effect on such a parabolic surface, see Geophysical fluid dynamics lab demonstration John Marshall, Massachusetts Institute of Technology.For a java applet of the Coriolis effect on such a parabolic surface, see Brian Fiedler School of Meteorology at the University of Oklahoma. Discs cut from cylinders of dry ice can be used as pucks, moving around almost frictionlessly over the surface of the parabolic turntable, allowing effects of Coriolis on dynamic phenomena to show themselves. To get a view of the motions as seen from the reference frame rotating with the turntable, a video camera is attached to the turntable so as to co-rotate with the turntable, with results as shown in the figure.

The filter operates on the edges of each 4×4 or 8×8 transform block in the luma and chroma planes of each picture. Each small block's edge is assigned a boundary strength based on whether it is also a macroblock boundary, the coding (intra/inter) of the blocks, whether references (in motion prediction and reference frame choice) differ, and whether it is a luma or chroma edge. Stronger levels of filtering are assigned by this scheme where there is likely to be more distortion. The filter can modify as many as three samples on either side of a given block edge (in the case where an edge is a luma edge that lies between different macroblocks and at least one of them is intra coded).

According to Cross, people of color are socialized to perceive an unracialized reference frame, and are thus resistant to any information that threatens this unracial perspective. In the encounter stage, individuals undergo an experience that suddenly and sharply calls race into perspective, and is generally an awakening to racial consciousness. This encounter makes the individual vulnerable to a new racialized worldview. Oftentimes, this occurrence is easily recalled as the first time a child was treated differently because of the color of his/her skin. The third stage, immersion-emersion, the individual acts as though he/she has “just discovered Blackness.” This individual often becomes adamant in “proving that one is black,” while taking an apparent pride in their blackness and simultaneously disparaging White culture.

But ET in principle did not yet take account of relativity theory. The size of the periodic part of the variations due to time dilation between earth-based atomic clocks and the coordinate time of the Solar-System barycentric reference frame had been estimated at under 2 milliseconds, but in spite of this small size, it was increasingly considered in the early 1970s that time standards should be made suitable for applications in which differences due to relativistic time dilation could no longer be neglected. In 1976, two new time scales were definedThey were defined in substance in 1976 but given their names in 1979. to replace ET (in the ephemerides for 1984 and afterwards) to take account of relativity.

The Cubist considerations manifested prior to the outset of World War I—such as the fourth dimension, dynamism of modern life, the occult, and Henri Bergson's concept of duration—had now been vacated, replaced by a purely formal reference frame. This clarity and sense of order spread to almost all of the artists under contract with Léonce Rosenberg—including Metzinger, Juan Gris, Jacques Lipchitz, Henri Laurens, Auguste Herbin, Joseph Csaky and Gino Severini—leading to the descriptive term 'Crystal Cubism', coined by the critic Maurice Raynal. By its very date of execution, Metzinger's Soldier at a Game of Chess was precursor to a style that would become known as Crystal Cubism.H. Harvard Arnason, History of Modern Art: Painting, Sculpture, Architecture, Photography, edited by Peter Kalb, Pub.

In the explicitly covariant formulation the transformation of the reference frame and the change of orientation of the light-front plane are decoupled. All the rotations and the Lorentz transformations are purely kinematical (they do not require knowledge of the interaction), whereas the (dynamical) dependence on the orientation of the light-front plane is covariantly parametrized by the wave function dependence on the four-vector \omega. There were formulated the rules of graph techniques which, for a given Lagrangian, allow to calculate the perturbative decomposition of the state vector evolving in the light-front time \sigma=\omega\cdot x (in contrast to the evolution in the direction x^+ or t). For the instant form of dynamics, these rules were first developed by Kadyshevsky.

A moving body's seeing no aberration in a static field emanating from a "motionless body" therefore causes Lorentz invariance to require that in the previously moving body's reference frame the (now moving) emitting body's field lines must not at a distance be retarded or aberred. Moving charged bodies (including bodies that emit static gravitational fields) exhibit static field lines that bend not with distance and show no speed of light delay effects, as seen from bodies moving with regard to them. In other words, since the gravitoelectric field is, by definition, static and continuous, it does not propagate. If such a source of a static field is accelerated (for example stopped) with regard to its formerly constant velocity frame, its distant field continues to be updated as though the charged body continued with constant velocity.

No computation of components is necessary (though they are rotated from the instrument reference frame into the conventional east-west and north-south components), and summing the components accomplishes the vector averaging. The advantages of a propeller with cosine response have been widely recognized.Walrod, R. A., 1970: Propeller current sensor response to off-axis flow, Masters thesis, Massachusetts Institute of Technology, 90 pp Weller and Davis designed the propeller sensors and their location within the pressure cage in order to obtain a response as close as possible to an ideal cosinusoidal angular response. After having fabricated and testes several families of propellers, they found the best response in a dual propeller (two propellers fixed on an axle) sensor with two five-bladed, 30-degree pitch propellers with diameter of 22 cm.

While each of the nine processing cores can sustain 25.6 GB/s read and write concurrently, the memory interface controller (MIC) is tied to a pair of XDR memory channels permitting a maximum flow of 25.6 GB/s for reads and writes combined and the two IO controllers are documented as supporting a peak combined input speed of 25.6 GB/s and a peak combined output speed of 35 GB/s. To add further to the confusion, some older publications cite EIB bandwidth assuming a 4 GHz system clock. This reference frame results in an instantaneous EIB bandwidth figure of 384 GB/s and an arbitration-limited bandwidth figure of 256 GB/s. All things considered the theoretic 204.8 GB/s number most often cited is the best one to bear in mind.

A charge moving with a constant velocity must appear to a distant observer in exactly the same way as a static charge appears to a moving observer, and in the latter case, the direction of the static field must change instantaneously, with no time-delay. Thus, static fields (the first term) point exactly at the true instantaneous (non-retarded) position of the charged object if its velocity has not changed over the retarded time delay. This is true over any distance separating objects. The second term, however, which contains information about the acceleration and other unique behavior of the charge that cannot be removed by changing the Lorentz frame (inertial reference frame of the observer), is fully dependent for direction on the time-retarded position of the source.

Optical tracking entails the use of a camera to relay positional information of objects within its inherent coordinate system by means of a subset of the electromagnetic spectrum of wavelengths spanning ultra-violet, visible, and infrared light. Optical navigation has been in use for the last 10 years within image-guided surgery (neurosurgery, ENT, and orthopaedic) and has increased in prevalence within radiotherapy to provide real-time feedback through visual cues on graphical user interfaces (GUIs). For the latter, a method of calibration is used to align the camera's native coordinate system with that of the isocentric reference frame of the radiation treatment delivery room. Optically tracked tools are then used to identify the positions of patient reference set-up points and these are compared to their location within the planning CT coordinate system.

Alice uses this device to send a message to Bob, who sends a reply. Let us choose the origin of the coordinates of Bob's reference frame, S, to coincide with the reception of Alice's message to him. If Bob immediately sends a message back to Alice, then in his rest frame the coordinates of the reply signal (in natural units so that c=1) are given by: :(t,x) = (t,at) To find out when the reply is received by Alice, we perform a Lorentz transformation to Alice's frame S' moving in the positive x-direction with velocity v with respect to the Earth. In this frame Alice is at rest at position x' = L, where L is the distance that the signal Alice sent to Earth traversed in her rest frame.

The change in angle is of the order of v/c where c is the speed of light and v the velocity of the observer. In the case of "stellar" or "annual" aberration, the apparent position of a star to an observer on Earth varies periodically over the course of a year as the Earth's velocity changes as it revolves around the Sun, by a maximum angle of approximately 20 arcseconds in right ascension or declination. The term aberration has historically been used to refer to a number of related phenomena concerning the propagation of light in moving bodies. Aberration is distinct from parallax, which is a change in the apparent position of a relatively nearby object, as measured by a moving observer, relative to more distant objects that define a reference frame.

In the proper reference frame of the bullet, the same result is obtained by noting that this frame is not inertial, which implies that the shape of the container will no more be flat, on the contrary, the sea floor becomes curved upwards, which results in the bullet getting far away the sea surface, i.e., in the bullet relatively sinking. The non-justified assumption considered by Supplee that the gravitational force on the bullet should depend on its energy content was eliminated by George Matsas, who used the full mathematical methods of general relativity in order to explain the Supplee paradox and agreed with Supplee's results. In particular, he modelled the situation using a Rindler chart, where a submarine is accelerated from the rest to a given velocity v.

Relativity of simultaneity: Event B is simultaneous with A in the green reference frame, but it occurred before in the blue frame, and occurs later in the red frame. Einstein showed in his thought experiments that people travelling at different speeds, while agreeing on cause and effect, measure different time separations between events, and can even observe different chronological orderings between non-causally related events. Though these effects are typically minute in the human experience, the effect becomes much more pronounced for objects moving at speeds approaching the speed of light. Subatomic particles exist for a well known average fraction of a second in a lab relatively at rest, but when travelling close to the speed of light they are measured to travel farther and exist for much longer than when at rest.

All inertial frames are in a state of constant, rectilinear motion with respect to one another; an accelerometer moving with any of them would detect zero acceleration. Measurements in one inertial frame can be converted to measurements in another by a simple transformation (the Galilean transformation in Newtonian physics and the Lorentz transformation in special relativity). In general relativity, in any region small enough for the curvature of spacetime and tidal forces Extract of page 219 to be negligible, one can find a set of inertial frames that approximately describe that region. In a non-inertial reference frame in classical physics and special relativity, the physics of a system vary depending on the acceleration of that frame with respect to an inertial frame, and the usual physical forces must be supplemented by fictitious forces.

The Datum of 2022 is a placeholder name for a new vertical datum set to be produced by the National Geodetic Survey in 2022 to improve the National Spatial Reference System (NSRS) by replacing the North American Datum of 1983 (NAD 83) and the North American Vertical Datum of 1988 (NAVD 88) with a new geometric reference frame and geopotential datum.New Datums: Replacing NAVD 88 and NAD 83 The new reference frames will rely primarily on Global Navigation Satellite Systems (GNSS), such as the Global Positioning System (GPS), as well as on a gravimetric geoid model resulting from NGS's Gravity for the Redefinition of the American Vertical Datum (GRAV-D) Project. These new reference frames are intended be easier to access and to maintain than NAD 83 and NAVD 88, which rely on physical survey marks that deteriorate over time.

In the limit of zero kinetic energy (or equivalently in the rest frame) of a massive particle, or else in the center of momentum frame for objects or systems which retain kinetic energy, the total energy of particle or object (including internal kinetic energy in systems) is related to its rest mass or its invariant mass via the famous equation E=mc^2. Thus, the rule of conservation of energy over time in special relativity continues to hold, so long as the reference frame of the observer is unchanged. This applies to the total energy of systems, although different observers disagree as to the energy value. Also conserved, and invariant to all observers, is the invariant mass, which is the minimal system mass and energy that can be seen by any observer, and which is defined by the energy–momentum relation.

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).

Modern geodetic reference systems, such as the World Geodetic System and the International Terrestrial Reference Frame, use a single oblate spheroid, fixed to the Earth's gravitational centre. The shift from several local spheroids to one worldwide spheroid caused all geographical coordinates to shift by many metres, sometimes as much as several hundred metres. The Prime Meridian of these modern reference systems is 102.5 metres east of the Greenwich astronomical meridian represented by the stainless steel strip, which is now 5.31 arcseconds West. The modern location of the Airy Transit is International time from the end of the 19th century until UT1 was based on Simon Newcomb's equations, giving a mean sun about 0.18 seconds behind UT1 (the equivalent of 2.7 arcseconds) as of 2013; it coincided in 2013 with a meridian halfway between Airy's circle and the IERS origin: .

Such analytical solutions are limited to relatively simple flow systems and reactions. Geochemical models, on the other hand, have been developed to provide thermodynamic descriptions of multicomponent systems without regard to transport. Reaction path models were created, for instance, to describe the sequence of chemical reactions resulting from chemical weathering or hydrothermal alteration in batch systems, in terms of the overall reaction progress. By adopting the reference frame of a packet of fluid and treating reaction progress as travel time (or distance along a flowpath), however, a batch reaction path model could be thought of as describing advective transport through an aquifer.Lichtner, P.C., 1988, The quasi-stationary state approximation to coupled mass transport and fluid-rock interaction in a porous medium. Geochemica et Cosmochemica Acta 52, 143-165 The most sophisticated multi-component reactive transport models consider both reaction and transport.

Thus, gravity acts like a fictitious force such as the centrifugal force or the Coriolis force, which result from being in an accelerated reference frame; all fictitious forces are proportional to the inertial mass, just as gravity is. To effect the reconciliation of gravity and special relativity and to incorporate the equivalence principle, something had to be sacrificed; that something was the long-held classical assumption that our space obeys the laws of Euclidean geometry, e.g., that the Pythagorean theorem is true experimentally. Einstein used a more general geometry, pseudo-Riemannian geometry, to allow for the curvature of space and time that was necessary for the reconciliation; after eight years of work (1907–1915), he succeeded in discovering the precise way in which space-time should be curved in order to reproduce the physical laws observed in Nature, particularly gravitation.

The spacetime coordinates of an event, as measured by each observer in their inertial reference frame (in standard configuration) are shown in the speech bubbles. Top: frame F′ moves at velocity v along the x-axis of frame F. Bottom: frame F moves at velocity −v along the x′-axis of frame F′.University Physics – With Modern Physics (12th Edition), H.D. Young, R.A. Freedman (Original edition), Addison-Wesley (Pearson International), 1st Edition: 1949, 12th Edition: 2008, The invariant interval can be seen as a non-positive definite distance function on spacetime. The set of transformations sought must leave this distance invariant. Due to the reference frame's coordinate system's cartesian nature, one concludes that, as in the Euclidean case, the possible transformations are made up of translations and rotations, where a slightly broader meaning should be allowed for the term rotation.

X. Li, P. Zhao, Q. J. Ge, and A. Purwar, A Task Driven Approach to Simultaneous Type Synthesis and Dimensional Optimization of Planar Parallel Manipulator Using Algebraic Fitting of a Family of Quadrics, ASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, Volume 6B: 37th Mechanisms and Robotics Conference Portland, Oregon, USA, August 4–7, 2013 Dimensional synthesis of linkages begins with a task defined as the movement of an output link relative to a base reference frame. This task may consist of the trajectory of a moving point or the trajectory of a moving body. The kinematics equations, or loop equations, of the mechanism must be satisfied in all of the required positions of the moving point or body. The result is a system of equations that are solved to compute the dimensions of the linkage.

This postulate is a subset of the postulates that underlie Maxwell's equations in the interpretation given to them in the context of special relativity. However, Maxwell's equations rely on several other postulates, some of which are now known to be false (e.g., Maxwell's equations cannot account for the quantum attributes of electromagnetic radiation). The second postulate can be used to imply a stronger version of itself, namely that the spacetime interval is invariant under changes of inertial reference frame. In the above notation, this means that :c^2 (s-t)^2 - (x_1-y_1)^2 - (x_2-y_2)^2 - (x_3-y_3)^2 := c^2 (s'-t')^2 - (x'_1-y'_1)^2 - (x'_2-y'_2)^2 - (x'_3-y'_3)^2 for any two events A, B. This can in turn be used to deduce the transformation laws between reference frames; see Lorentz transformation.

Its activities abroad begin into 1986 within a new subsidiary private company IGN France International. From 2000, the IGN develops the concept of Reference frame on a Large Scale (référentiel à grande échelle = RGE); it is a question of completing within a deadline short digitalization the cartography of the French territory with a meter scale and according to four components: topography, land registry and address. This RGE is entirely completed at the end of 2008. Then it enter in a cycle of maintenance In June 2006, the IGN opened the service Géoportail allowing the cartographic visualization of the French territory on a Web navigator and using on one hand funds of air photographs and on the other hand the digitized maps to the 1/25 000. “Phase 2” of Géoportail was put on line one year later, with a new ergonomics.

Henri Poincaré gave a physical interpretation to local time (to first order in v/c, the relative velocity of the two reference frames normalized to the speed of light) as the consequence of clock synchronization, under the assumption that the speed of light is constant in moving frames. Larmor is credited to have been the first to understand the crucial time dilation property inherent in his equations. In 1905, Poincaré was the first to recognize that the transformation has the properties of a mathematical group, and named it after Lorentz.The reference is within the following paper: Later in the same year Albert Einstein published what is now called special relativity, by deriving the Lorentz transformation under the assumptions of the principle of relativity and the constancy of the speed of light in any inertial reference frame, and by abandoning the mechanistic aether as unnecessary.

A complex horseshoe orbit (the vertical looping is due to inclination of the smaller body's orbit to that of the Earth, and would be absent if both orbited in the same plane) A horseshoe orbit is a type of co-orbital motion of a small orbiting body relative to a larger orbiting body. The orbital period of the smaller body is very nearly the same as for the larger body, and its path appears to have a horseshoe shape as viewed from the larger object in a rotating reference frame. The loop is not closed but will drift forward or backward slightly each time, so that the point it circles will appear to move smoothly along the larger body's orbit over a long period of time. When the object approaches the larger body closely at either end of its trajectory, its apparent direction changes.

The Cubist considerations manifested prior to the outset of World War I—such as the fourth dimension, dynamism of modern life, the occult, and Henri Bergson's concept of duration—had now been vacated, replaced by a purely formal reference frame. This clarity and sense of order spread to almost all on the artists under contract with Léonce Rosenberg—including Juan Gris, Jacques Lipchitz, Henri Laurens, Auguste Herbin, Joseph Csaky and Gino Severini—leading to the descriptive term 'Crystal Cubism', coined by the critic Maurice Raynal. Femme au miroir, as other works by Metzinger of the same period, relate to those of his colleague and friend Juan Gris, whose Portrait of Josette Gris was painted just six months after Metzinger's canvas, and with Gris' Seated Woman of 1917. The works of Gris and Metzinger painted during the war employ transparencies that blur the distinction between the background and the figure.

EBEX 2012, a high-altitude balloon-borne cosmology experiment launched from Antarctica on 2012-12-29 A star tracker is an optical device that measures the positions of stars using photocells or a camera. As the positions of many stars have been measured by astronomers to a high degree of accuracy, a star tracker on a satellite or spacecraft may be used to determine the orientation (or attitude) of the spacecraft with respect to the stars. In order to do this, the star tracker must obtain an image of the stars, measure their apparent position in the reference frame of the spacecraft, and identify the stars so their position can be compared with their known absolute position from a star catalog. A star tracker may include a processor to identify stars by comparing the pattern of observed stars with the known pattern of stars in the sky.

Cosmology ABC Catalyst segment on Cosmology, with Brian Schmidt, Ray Norris, & Lawrence Krauss The team's observations were contrary to the then-current models, which predicted that the expansion of the universe should be slowing down, and when the preliminary results emerged Schmidt assumed it was an error and he spent the next six weeks trying to find the mistake. But there was no mistake: contrary to expectations, by monitoring the brightness and measuring the redshift of the supernovae, they discovered that these billion-year old exploding stars and their galaxies were accelerating away from our reference frame. This result was also found nearly simultaneously by the Supernova Cosmology Project, led by Saul Perlmutter. The corroborating evidence between the two competing studies led to the acceptance of the accelerating universe theory and initiated new research to understand the nature of the universe, such as the existence of dark energy.

Fan letters in the magazine complained about the novel's containment within the solar system, and Sloane sided with the readers. So when Harry Bates, editor of Astounding Stories, offered Smith 2¢/word—payable on publication—for his next story, he agreed; this meant that it could not be a sequel to Spacehounds. This book would be Triplanetary, "in which scientific detail would not be bothered about, and in which his imagination would run riot."Warner. Indeed, characters within the story point out its psychologicalLyman Cleveland's comment on the easy availability of "solid asteroids of iron", Amazing March 1934, p. 16, first edition p.196, as proving the pointlessness of the Nevians' attack. and scientificCleveland's expectation, correct according to special relativity, that inertialess travel would not be faster than light in the home reference frame, p. 223. implausibilities, and sometimes even seem to suggest self-parody.

In June 2016, NASA and ESA scientists reported that the universe was found to be expanding 5% to 9% faster than thought earlier, based on studies using the Hubble Space Telescope. While special relativity prohibits objects from moving faster than light with respect to a local reference frame where spacetime can be treated as flat and unchanging, it does not apply to situations where spacetime curvature or evolution in time become important. These situations are described by general relativity, which allows the separation between two distant objects to increase faster than the speed of light, although the definition of "separation" is different from that used in an inertial frame. This can be seen when observing distant galaxies more than the Hubble radius away from us (approximately 4.5 gigaparsecs or 14.7 billion light-years); these galaxies have a recession speed that is faster than the speed of light.

Time has historically been closely related with space, the two together merging into spacetime in Einstein's special relativity and general relativity. According to these theories, the concept of time depends on the spatial reference frame of the observer, and the human perception as well as the measurement by instruments such as clocks are different for observers in relative motion. For example, if a spaceship carrying a clock flies through space at (very nearly) the speed of light, its crew does not notice a change in the speed of time on board their vessel because everything traveling at the same speed slows down at the same rate (including the clock, the crew's thought processes, and the functions of their bodies). However, to a stationary observer watching the spaceship fly by, the spaceship appears flattened in the direction it is traveling and the clock on board the spaceship appears to move very slowly.

The total amount of some conserved quantity in the universe could remain unchanged if an equal amount were to appear at one point A and simultaneously disappear from another separate point B. For example, an amount of energy could appear on Earth without changing the total amount in the Universe if the same amount of energy were to disappear from a remote region of the Universe. This weak form of "global" conservation is really not a conservation law because it is not Lorentz invariant, so phenomena like the above do not occur in nature. Due to special relativity, if the appearance of the energy at A and disappearance of the energy at B are simultaneous in one inertial reference frame, they will not be simultaneous in other inertial reference frames moving with respect to the first. In a moving frame one will occur before the other; either the energy at A will appear before or after the energy at B disappears.

This line passes through A and B, so A and B are simultaneous from the reference frame of the observer with black axes. However, the clock that is moving relative to the black observer marks off time along the blue time axis. This is represented by the distance from O to B. Therefore, the observer at A with the black axes notices their clock as reading the distance from O to A while they observe the clock moving relative him or her to read the distance from O to B. Due to the distance from O to B being smaller than the distance from O to A, they conclude that the time passed on the clock moving relative to them is smaller than that passed on their own clock. A second observer, having moved together with the clock from O to B, will argue that the other clock has reached only C until this moment and therefore this clock runs slower.

Albert Einstein went through several versions of light speed theory between 1905 and 1915, eventually concluding that light speed is constant when gravity does not have to be considered but that the speed of light cannot be constant in a gravitational field with variable strength. In the same book Einstein explained that he intended light speed to be a vector when it was described by coordinates in a reference frame. Einstein was not explicit about whether the speed of light would change in a gravity field, or whether just the direction of the vector would change; this can be clarified from the text implicitly, however. A calculation of alpha (α) follows equation 107 and makes an unambiguous use of variable scalar light velocity (L) both as the argument of a partial differential function (proving a variable) and as the denominator in a fraction (proving not a vector) both in the same integrated quantity.

With these advances there also arose the necessity to define a reference meridian that, whilst being derived from the Airy Transit Circle, would also take into account the effects of plate movement and variations in the way that the Earth was spinning. As a result, the International Reference Meridian was established and is commonly used to denote Earth's prime meridian (0° longitude) by the International Earth Rotation and Reference Systems Service, which defines and maintains the link between longitude and time. Based on observations to satellites and celestial compact radio sources (quasars) from various coordinated stations around the globe, Airy's transit circle drifts northeast about 2.5 centimetres per year relative to this Earth-centred 0° longitude. It is also the reference meridian of the Global Positioning System operated by the United States Department of Defense, and of WGS84 and its two formal versions, the ideal International Terrestrial Reference System (ITRS) and its realization, the International Terrestrial Reference Frame (ITRF).

The Gaia catalogue is released in stages that will contain increasing amounts of information; the early releases also miss some stars, especially fainter stars located in dense star fields and members of close binary pairs. The first data release, Gaia DR1, based on 14 months of observations made through September 2015, took place on 14 September 2016 and is described in a series of articles published in Astronomy and Astrophysics. The data release includes "positions and … magnitudes for 1.1 billion stars using only Gaia data; positions, parallaxes and proper motions for more than 2 million stars" based on a combination of Gaia and Tycho-2 data for those objects in both catalogues; "light curves and characteristics for about 3000 variable stars; and positions and magnitudes for more than 2000 … extragalactic sources used to define the celestial reference frame". Data from this DR1 release can be accessed at the Gaia archive, as well as through astronomical data centers such as CDS.

The convention that EM radiation that is known to come from the nucleus, is always called "gamma ray" radiation is the only convention that is universally respected, however. Many astronomical gamma ray sources (such as gamma ray bursts) are known to be too energetic (in both intensity and wavelength) to be of nuclear origin. Quite often, in high energy physics and in medical radiotherapy, very high energy EMR (in the >10 MeV region)—which is of higher energy than any nuclear gamma ray—is not called X-ray or gamma-ray, but instead by the generic term of "high energy photons." The region of the spectrum where a particular observed electromagnetic radiation falls, is reference frame-dependent (due to the Doppler shift for light), so EM radiation that one observer would say is in one region of the spectrum could appear to an observer moving at a substantial fraction of the speed of light with respect to the first to be in another part of the spectrum.

Based on the definition of Neumann, Heinrich Streintz (1883) argued that in a coordinate system where gyroscopes do not measure any signs of rotation inertial motion is related to a "Fundamental body" and a "Fundamental Coordinate System". Eventually, Ludwig Lange (1885) was the first to coin the expression inertial frame of reference and "inertial time scale" as operational replacements for absolute space and time; he defined "inertial frame" as "a reference frame in which a mass point thrown from the same point in three different (non-co-planar) directions follows rectilinear paths each time it is thrown". In 1902, Henri Poincaré published a collection of essays titled Science and Hypothesis, which included: detailed philosophical discussions on the relativity of space, time, and on the conventionality of distant simultaneity; the conjecture that a violation of the relativity principle can never be detected; the possible non-existence of the aether, together with some arguments supporting the aether; and many remarks on non- Euclidean vs. Euclidean geometry.

Between the mirrors a light signal is bouncing, and for the observer resting in the same reference frame as A, the period of clock A is the distance between the mirrors divided by the speed of light. But if the observer looks at clock B, he sees that within that clock the signal traces out a longer, angled path, thus clock B is slower than A. However, for the observer moving alongside with B the situation is completely in reverse: Clock B is faster and A is slower. Also Lorentz (1910–1912) discussed the reciprocity of time dilation and analyzed a clock "paradox", which apparently occurs as a consequence of the reciprocity of time dilation. Lorentz showed that there is no paradox if one considers that in one system only one clock is used, while in the other system two clocks are necessary, and the relativity of simultaneity is fully taken into account.

Einstein (1908) tried – as a preliminary in the framework of special relativity – also to include accelerated frames within the relativity principle. In the course of this attempt he recognized that for any single moment of acceleration of a body one can define an inertial reference frame in which the accelerated body is temporarily at rest. It follows that in accelerated frames defined in this way, the application of the constancy of the speed of light to define simultaneity is restricted to small localities. However, the equivalence principle that was used by Einstein in the course of that investigation, which expresses the equality of inertial and gravitational mass and the equivalence of accelerated frames and homogeneous gravitational fields, transcended the limits of special relativity and resulted in the formulation of general relativity.Pais (2000), 177-183 Nearly simultaneously with Einstein, also Minkowski (1908) considered the special case of uniform accelerations within the framework of his space-time formalism.

The name arises because the Z-matrix assigns the second atom along the Z axis from the first atom, which is at the origin. Z-matrices can be converted to Cartesian coordinates and back, as the structural information content is identical, the position and orientation in space, however is not meaning the Cartesian coordinates recovered will be accurate in terms of relative positions of atoms, but will not necessarily be the same as an original set of Cartesian coordinates if you convert Cartesian coordinates to a Z matrix and back again. While the transform is conceptually straightforward, algorithms of doing the conversion vary significantly in speed, numerical precision and parallelism. These matter because macromolecular chains, such as polymers, proteins, and DNA, can have thousands of connected atoms and atoms consecutively distant along the chain that may be close in Cartesian space (and thus small round-off errors can accumulate to large force-field errors.) The optimally fastest and most numerically accurate algorithm for conversion from torsion-space to cartesian- space is the Natural Extension Reference Frame method.

Einstein proposed that gravitation is a result of masses (or their equivalent energies) curving ("bending") the spacetime in which they exist, altering the paths they follow within it. Einstein argued that the speed of light was a constant in all inertial reference frames and that electromagnetic laws should remain valid independent of reference frame—assertions which rendered the ether "superfluous" to physical theory, and that held that observations of time and length varied relative to how the observer was moving with respect to the object being measured (what came to be called the "special theory of relativity"). It also followed that mass and energy were interchangeable quantities according to the equation E=mc2. In another paper published the same year, Einstein asserted that electromagnetic radiation was transmitted in discrete quantities ("quanta"), according to a constant that the theoretical physicist Max Planck had posited in 1900 to arrive at an accurate theory for the distribution of blackbody radiation—an assumption that explained the strange properties of the photoelectric effect.

The divers Cubist considerations manifested prior to World War I—such as the fourth dimension, dynamism of modern life, and Henri Bergson's concept of duration—had now been replaced by a formal reference frame which constituted the second phase of Cubism, based upon an elementary set of principles that formed a cohesive Cubist aesthetic. This clarity and sense of order spread to almost all of the artists exhibiting at Léonce Rosenberg's gallery—including Jean Metzinger, Juan Gris, Jacques Lipchitz, Henri Laurens, Auguste Herbin, Joseph Csaky, Gino Severini and Pablo Picasso—leading to the descriptive term 'Crystal Cubism', coined by Maurice Raynal, an early promoter of Cubism and continuous supporter during the war and post-war phase that followed.Anna Jozefacka, Leonard A. Lauder, Research Center for Modern Art, The Metropolitan Museum of Art, January 2015 Raynal had been associated with Cubists since 1910 via the milieu of Le Bateau-Lavoir. David Cottington, Cubism in the Shadow of War: The Avant-garde and Politics in Paris 1905-1914, Yale University Press, 1998, p.

The second component is commonly referred to as true polar wander (TPW) and on geologic time scales results from gradual redistribution of mass heterogeneities due to convective motions in the Earth's mantle. By comparing plate reconstructions based on paleomagnetism with reconstructions in the mantle reference frame defined by hotspots for the last 120 Ma, the TPW motions can be estimated, which allows tying paleogeographic reconstructions to the mantle and hence constraining them in paleolongitude. For the earlier times in the Mesozoic and Paleozoic, TPW estimates can be obtained through the analysis of coherent rotations of the continental lithosphere, which allows linking the reconstructed paleogeography to the large-scale structures in the lower mantle, commonly referred to as Large Low Shear-wave Velocity Provinces (LLSVPs). It has been argued that the LLSVPs have been stable over at least the past 300 Ma, and possibly longer, and that the LLSVP margins have served as generation zones for the mantle plumes responsible for eruptions of Large Igneous Provinces (LIPs) and kimberlites.

Clocks that are far from massive bodies (or at higher gravitational potentials) run more quickly, and clocks close to massive bodies (or at lower gravitational potentials) run more slowly. For example, considered over the total time-span of Earth (4.6 billion years), a clock set in a geostationary position at an altitude of 9,000 meters above sea level, such as perhaps at the top of Mount Everest (prominence 8,848m), would be about 39 hours ahead of a clock set at sea level. Extract of page 433 Extract of page 118 This is because gravitational time dilation is manifested in accelerated frames of reference or, by virtue of the equivalence principle, in the gravitational field of massive objects.John A. Auping, Proceedings of the International Conference on Two Cosmological Models, Plaza y Valdes, According to general relativity, inertial mass and gravitational mass are the same, and all accelerated reference frames (such as a uniformly rotating reference frame with its proper time dilation) are physically equivalent to a gravitational field of the same strength.

At the end of the early universe's inflationary period, all the matter and energy in the universe was set on an inertial trajectory consistent with the equivalence principle and Einstein's general theory of relativity and this is when the precise and regular form of the universe's expansion had its origin (that is, matter in the universe is separating because it was separating in the past due to the inflaton field). While special relativity prohibits objects from moving faster than light with respect to a local reference frame where spacetime can be treated as flat and unchanging, it does not apply to situations where spacetime curvature or evolution in time become important. These situations are described by general relativity, which allows the separation between two distant objects to increase faster than the speed of light, although the definition of "distance" here is somewhat different from that used in an inertial frame. The definition of distance used here is the summation or integration of local comoving distances, all done at constant local proper time.

It is needed within the passenger's local frame of reference to explain his sudden tendency to start accelerating to the right relative to the car—a tendency which he must resist by applying a rightward force to the car (for instance, a frictional force against the seat) in order to remain in a fixed position inside. Since he pushes the seat toward the right, Newton's third law says that the seat pushes him toward the left. The centrifugal force must be included in the passenger's reference frame (in which the passenger remains at rest): it counteracts the leftward force applied to the passenger by the seat, and explains why this otherwise unbalanced force does not cause him to accelerate. However, it would be apparent to a stationary observer watching from an overpass above that the frictional force exerted on the passenger by the seat is not being balanced; it constitutes a net force to the left, causing the passenger to accelerate toward the inside of the curve, as he must in order to keep moving with the car rather than proceeding in a straight line as he otherwise would.

Two-dimensional visualization of an Alcubierre drive, showing the opposing regions of expanding and contracting spacetime that displace the central region The Alcubierre drive, Alcubierre warp drive, or Alcubierre metric (referring to metric tensor) is a speculative idea based on a solution of Einstein's field equations in general relativity as proposed by theoretical physicist Miguel Alcubierre, by which a spacecraft could achieve apparent faster-than-light travel if a configurable energy-density field lower than that of vacuum (that is, negative mass) could be created. Rather than exceeding the speed of light within a local reference frame, a spacecraft would traverse distances by contracting space in front of it and expanding space behind it, resulting in effective faster-than-light travel. Objects cannot accelerate to the speed of light within normal spacetime; instead, the Alcubierre drive shifts space around an object so that the object would arrive at its destination faster than light would in normal space without breaking any physical laws. Although the metric proposed by Alcubierre is consistent with the Einstein field equations, construction of such a drive is not necessarily possible.