Inertial frame of reference

3034:. The flatness of the Milky Way depends on its rate of rotation in an inertial frame of reference. If its apparent rate of rotation is attributed entirely to rotation in an inertial frame, a different "flatness" is predicted than if it is supposed that part of this rotation is actually due to rotation of the universe and should not be included in the rotation of the galaxy itself. Based upon the laws of physics, a model is set up in which one parameter is the rate of rotation of the Universe. If the laws of physics agree more accurately with observations in a model with rotation than without it, we are inclined to select the best-fit value for rotation, subject to all other pertinent experimental observations. If no value of the rotation parameter is successful and theory is not within observational error, a modification of physical law is considered, for example, 4443:, employed for navigation of seagoing vessels, finds the geometric north. It does so, not by sensing the Earth's magnetic field, but by using inertial space as its reference. The outer casing of the gyrocompass device is held in such a way that it remains aligned with the local plumb line. When the gyroscope wheel inside the gyrocompass device is spun up, the way the gyroscope wheel is suspended causes the gyroscope wheel to gradually align its spinning axis with the Earth's axis. Alignment with the Earth's axis is the only direction for which the gyroscope's spinning axis can be stationary with respect to the Earth and not be required to change direction with respect to inertial space. After being spun up, a gyrocompass can reach the direction of alignment with the Earth's axis in as little as a quarter of an hour. 1553:). Another approach is to identify all real sources for real forces and account for them. A possible issue with this approach is the possibility of missing something, or accounting inappropriately for their influence, perhaps, again, due to Mach's principle and an incomplete understanding of the universe. A third approach is to look at the way the forces transform when shifting reference frames. Fictitious forces, those that arise due to the acceleration of a frame, disappear in inertial frames and have complicated rules of transformation in general cases. Based on the universality of physical law and the request for frames where the laws are most simply expressed, inertial frames are distinguished by the absence of such fictitious forces. 739: 4383:

stationary spheres from a rotating frame), the zero tension in the string is accounted for by observing that the centripetal force is supplied by the centrifugal and Coriolis forces in combination, so no tension is needed. If the spheres really are rotating, the tension observed is exactly the centripetal force required by the circular motion. Thus, measurement of the tension in the string identifies the inertial frame: it is the one where the tension in the string provides exactly the centripetal force demanded by the motion as it is observed in that frame, and not a different value. That is, the inertial frame is the one where the fictitious forces vanish.

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suppose that your watch is running five minutes fast compared to the local standard time. If you know that this is the case, when somebody asks you what time it is, you can deduct five minutes from the time displayed on your watch to obtain the correct time. The measurements that an observer makes about a system depend therefore on the observer's frame of reference (you might say that the bus arrived at 5 past three, when in fact it arrived at three).

4276: 752: 1650: 4265: 4379:, no originating bodies. A second approach is to look at a variety of frames of reference. For any inertial frame, the Coriolis force and the centrifugal force disappear, so application of the principle of special relativity would identify these frames where the forces disappear as sharing the same and the simplest physical laws, and hence rule that the rotating frame is not an inertial frame. 3653: 3507: 4452: 1389: 4224: 2481:, which determines whether the ratio of inertial to gravitational mass is the same for all bodies, regardless of size or composition. To date no difference has been found to a few parts in 10. For some discussion of the subtleties of the Eötvös experiment, such as the local mass distribution around the experimental site (including a quip about the mass of Eötvös himself), see Franklin. 2853: 3872: 2203:, that is, 25 seconds, as before. Note how much easier the problem becomes by choosing a suitable frame of reference. The third possible frame of reference would be attached to the second car. That example resembles the case just discussed, except the second car is stationary and the first car moves backward towards it at 4374:

For example, consider a stationary object in an inertial frame. Being at rest, no net force is applied. But in a frame rotating about a fixed axis, the object appears to move in a circle, and is subject to centripetal force. How can it be decided that the rotating frame is a non-inertial frame? There

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For a simple example involving only the orientation of two observers, consider two people standing, facing each other on either side of a north-south street. See Figure 2. A car drives past them heading south. For the person facing east, the car was moving to the right. However, for the person facing

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That is, the universality of the laws of physics requires the same tension to be seen by everybody. For example, it cannot happen that the string breaks under extreme tension in one frame of reference and remains intact in another frame of reference, just because we choose to look at the string from

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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

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For these ideas to apply, everything observed in the frame has to be subject to a base-line, common acceleration shared by the frame itself. That situation would apply, for example, to the elevator example, where all objects are subject to the same gravitational acceleration, and the elevator itself

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This principle generalizes the notion of an inertial frame. For example, an observer confined in a free-falling lift will assert that he himself is a valid inertial frame, even if he is accelerating under gravity, so long as he has no knowledge about anything outside the lift. So, strictly speaking,

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It would have been possible to choose a rotating, accelerating frame of reference, moving in a complicated manner, but this would have served to complicate the problem unnecessarily. It is also necessary to note that one can convert measurements made in one coordinate system to another. For example,

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Consider a situation common in everyday life. Two cars travel along a road, both moving at constant velocities. See Figure 1. At some particular moment, they are separated by 200 meters. The car in front is traveling at 22 meters per second and the car behind is traveling at 30 meters per second. If

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When there is accelerated motion due to a force being exerted there is manifestation of inertia. If an electric car designed to recharge its battery system when decelerating is switched to braking, the batteries are recharged, illustrating the physical strength of manifestation of inertia. However,

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rotation. However, if rotation were found, interpretation of observations in a frame tied to the universe would have to be corrected for the fictitious forces inherent in such rotation in classical physics and special relativity, or interpreted as the curvature of spacetime and the motion of matter

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is an indication of zero net force, the rule does not identify inertial reference frames because straight-line motion can be observed in a variety of frames. If the rule is interpreted as defining an inertial frame, then being able to determine when zero net force is applied is crucial. The problem

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The laws of Newtonian mechanics do not always hold in their simplest form...If, for instance, an observer is placed on a disc rotating relative to the earth, he/she will sense a 'force' pushing him/her toward the periphery of the disc, which is not caused by any interaction with other bodies. Here,

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In practice, using a frame of reference based upon the fixed stars as though it were an inertial frame of reference introduces little discrepancy. For example, the centrifugal acceleration of the Earth because of its rotation about the Sun is about thirty million times greater than that of the Sun

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There are several approaches to this issue. One approach is to argue that all real forces drop off with distance from their sources in a known manner, so it is only needed that a body is far enough away from all sources to ensure that no force is present. A possible issue with this approach is the

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In practical terms, the equivalence of inertial reference frames means that scientists within a box moving with a constant absolute velocity cannot determine this velocity by any experiment. Otherwise, the differences would set up an absolute standard reference frame. According to this definition,

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in two ways: first, it is restricted to mechanics, and second, it makes no mention of simplicity. It shares the special principle of the invariance of the form of the description among mutually translating reference frames. The role of fictitious forces in classifying reference frames is pursued

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at a speed of 117 km/s. The concept of inertial frames of reference is no longer tied to either the fixed stars or to absolute space. Rather, the identification of an inertial frame is based on the simplicity of the laws of physics in the frame. The laws of nature take a simpler form in

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Newton examined this problem himself using rotating spheres, as shown in Figure 2 and Figure 3. He pointed out that if the spheres are not rotating, the tension in the tying string is measured as zero in every frame of reference. If the spheres only appear to rotate (that is, we are watching

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of all observed double star systems remains fixed with respect to the direction of the angular momentum of the Solar System. These observations allowed him to conclude that inertial frames inside the galaxy do not rotate with respect to one another, and that the space of the Milky Way is

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the manifestation of inertia does not prevent acceleration (or deceleration), for manifestation of inertia occurs in response to change in velocity due to a force. Seen from the perspective of a rotating frame of reference the manifestation of inertia appears to exert a force (either in

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For a more complex example involving observers in relative motion, consider Alfred, who is standing on the side of a road watching a car drive past him from left to right. In his frame of reference, Alfred defines the spot where he is standing as the origin, the road as the

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the acceleration is not the consequence of the usual force, but of the so-called inertial force. Newton's laws hold in their simplest form only in a family of reference frames, called inertial frames. This fact represents the essence of the Galilean principle of relativity:

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inertial frame is a relative concept. With this in mind, inertial frames can collectively be defined as a set of frames which are stationary or moving at constant velocity with respect to each other, so that a single inertial frame is defined as an element of this set.

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The weakness of the principle of inertia lies in this, that it involves an argument in a circle: a mass moves without acceleration if it is sufficiently far from other bodies; we know that it is sufficiently far from other bodies only by the fact that it moves without

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Special principle of relativity: If a system of coordinates K is chosen so that, in relation to it, physical laws hold good in their simplest form, the same laws hold good in relation to any other system of coordinates K' moving in uniform translation relatively to

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were supposed to hold. In contrast, in frames accelerating with respect to the fixed stars, an important case being 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

3668: 1636:. The predictions of special relativity have been extensively verified experimentally. The Lorentz transformation reduces to the Galilean transformation as the speed of light approaches infinity or as the relative velocity between frames approaches zero. 3958: 2507:, where curvature effects become less important and the earlier inertial frame arguments can come back into play. Consequently, modern special relativity is now sometimes described as only a "local theory". "Local" can encompass, for example, the entire 4049: 4432:

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. Thus, inertial navigation is a form of

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observed the motion of pairs of stars orbiting each other. He found that the two orbits of the stars of such a system lie in a plane, and the perihelion of the orbits of the two stars remains pointing in the same direction with respect to the

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The original question, "relative to what frame of reference do the laws of motion hold?" is revealed to be wrongly posed. The laws of motion essentially determine a class of reference frames, and (in principle) a procedure for constructing

2220: 3648:{\displaystyle \mathbf {a} '=\mathbf {a} -{\dot {\boldsymbol {\omega }}}\times \mathbf {r} '-2{\boldsymbol {\omega }}\times \mathbf {v} '-{\boldsymbol {\omega }}\times ({\boldsymbol {\omega }}\times \mathbf {r} ')-\mathbf {A} _{0}.} 3502:{\displaystyle \mathbf {a} =\mathbf {a} '+{\dot {\boldsymbol {\omega }}}\times \mathbf {r} '+2{\boldsymbol {\omega }}\times \mathbf {v} '+{\boldsymbol {\omega }}\times ({\boldsymbol {\omega }}\times \mathbf {r} ')+\mathbf {A} _{0},} 4219:{\displaystyle \mathbf {F} '_{\mathrm {centrifugal} }=-m{\boldsymbol {\omega }}\times ({\boldsymbol {\omega }}\times \mathbf {r} ')=m(\omega ^{2}\mathbf {r} '-({\boldsymbol {\omega }}\cdot \mathbf {r} '){\boldsymbol {\omega }})} 1281: 1069:. An inertial frame was then one in uniform translation relative to absolute space. However, some "relativists", even at the time of Newton, felt that absolute space was a defect of the formulation, and should be replaced. 4395:

If bodies, any how moved among themselves, are urged in the direction of parallel lines by equal accelerative forces, they will continue to move among themselves, after the same manner as if they had been urged by no such

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would not work for the rotating observer without invoking centrifugal and Coriolis forces to account for their observations (tension in the case of the spheres; parabolic water surface in the case of the rotating bucket).

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are two approaches to this resolution: one approach is to look for the origin of the fictitious forces (the Coriolis force and the centrifugal force). It will be found there are no sources for these forces, no associated

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Here the relation between inertial and non-inertial observational frames of reference is considered. The basic difference between these frames is the need in non-inertial frames for fictitious forces, as described below.

3342: 2848:{\displaystyle \mathbf {F} '=\mathbf {F} -2m\mathbf {\Omega } \times \mathbf {v} _{B}-m\mathbf {\Omega } \times (\mathbf {\Omega } \times \mathbf {x} _{B})-m{\frac {d\mathbf {\Omega } }{dt}}\times \mathbf {x} _{B}\ ,} 2966:. Two experiments were devised by Newton to demonstrate how these forces could be discovered, thereby revealing to an observer that they were not in an inertial frame: the example of the tension in the cord linking 1888: 4319:

The equations of motion in a non-inertial system differ from the equations in an inertial system by additional terms called inertial forces. This allows us to detect experimentally the non-inertial nature of a

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The utility of operational definitions was carried much further in the special theory of relativity. Some historical background including Lange's definition is provided by DiSalle, who says in summary:

2915:= 0; that is, they are zero for an inertial frame (which, of course, does not rotate); they take on a different magnitude and direction in every rotating frame, depending upon its particular value of 93: 117: 5652: 3359:

A common sort of accelerated reference frame is a frame that is both rotating and translating (an example is a frame of reference attached to a CD which is playing while the player is carried).

2686: 5467: 3867:{\displaystyle \mathbf {F} '=\mathbf {F} _{\mathrm {physical} }+\mathbf {F} '_{\mathrm {Euler} }+\mathbf {F} '_{\mathrm {Coriolis} }+\mathbf {F} '_{\mathrm {centripetal} }-m\mathbf {A} _{0},} 1108:

The existence of absolute space contradicts the internal logic of classical mechanics since, according to the Galilean principle of relativity, none of the inertial frames can be singled out.

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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, is called an inertial frame.

2589: 2283:-axis. In this frame of reference, it is Betsy who is stationary and the world around her that is moving – for instance, as she drives past Alfred, she observes him moving with velocity 2128: 1430: 1215: 2919:; they are ubiquitous in the rotating frame (affect every particle, regardless of circumstance); and they have no apparent source in identifiable physical sources, in particular, 1330: 6212: 2462:

There is no experiment observers can perform to distinguish whether an acceleration arises because of a gravitational force or because their reference frame is accelerating.

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Now consider Betsy, the person driving the car. Betsy, in choosing her frame of reference, defines her location as the origin, the direction to her right as the positive

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This idea was introduced in Einstein's 1907 article "Principle of Relativity and Gravitation" and later developed in 1911. Support for this principle is found in the

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An accelerated frame of reference is often delineated as being the "primed" frame, and all variables that are dependent on that frame are notated with primes, e.g.

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as follows. We stand on the side of the road and start a stop-clock at the exact moment that the second car passes us, which happens to be when they are a distance

4282:: Exploded view of rotating spheres in an inertial frame of reference showing the centripetal forces on the spheres provided by the tension in the tying string. 1995: 783: 2268:-direction. Alfred's frame of reference is considered an inertial frame because he is not accelerating, ignoring effects such as Earth's rotation and gravity. 2231:

west, the car was moving to the left. This discrepancy is because the two people used two different frames of reference from which to investigate this system.

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The motions of bodies included in a given space are the same among themselves, whether that space is at rest or moves uniformly forward in a straight line.

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To apply the Newtonian definition of an inertial frame, the understanding of separation between "fictitious" forces and "real" forces must be made clear.

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we want to find out how long it will take the second car to catch up with the first, there are three obvious "frames of reference" that we could choose.

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provided a body not subject to forces appears to move in a straight line. If that motion is seen in one frame, it will also appear that way in the other.

2938:; only non-inertial observers need fictitious forces. The laws of physics in the inertial frame are simpler because unnecessary forces are not present. 1223: 491: 5037: 5464: 4271:: Two spheres tied with a string and rotating at an angular rate ω. Because of the rotation, the string tying the spheres together is under tension. 464: 2931:). For example, the centrifugal force that appears to emanate from the axis of rotation in a rotating frame increases with distance from the axis. 966:

The motion of a body can only be described relative to something else—other bodies, observers, or a set of spacetime coordinates. These are called

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postulate the equivalence of all inertial reference frames. The Galilean transformation transforms coordinates from one inertial reference frame,

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is constant, she is in an inertial frame of reference, and she will find the acceleration to be the same as Alfred in her frame of reference,

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inertial frames of reference because in these frames one did not have to introduce inertial forces when writing down Newton's law of motion.

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This simplicity manifests itself in that inertial frames have self-contained physics without the need for external causes, while physics in

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showing scenes as viewed from both an inertial frame and a rotating frame of reference, visualizing the Coriolis and centrifugal forces.

446: 2990:. Those that are outside our galaxy (such as nebulae once mistaken to be stars) participate in their own motion as well, partly due to 5855: 5672: 4975: 4764: 2442: 1488:

An inertial frame of reference is one in which the motion of a particle not subject to forces is in a straight line at constant speed.

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Newton viewed the first law as valid in any reference frame that is in uniform motion (neither rotating nor accelerating) relative to

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Absolute space does not explain inertial forces since they are related to acceleration with respect to any one of the inertial frames.

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Finally, as an example of non-inertial observers, assume Candace is accelerating her car. As she passes by him, Alfred measures her

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The effect of this being in the noninertial frame is to require the observer to introduce a fictitious force into his calculations…

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with a metric that produces non-zero curvature. In general relativity, the principle of inertia is replaced with the principle of

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The vector from the origin of an inertial reference frame to the origin of an accelerated reference frame is commonly notated as

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situated in the first car. In this case, the first car is stationary and the second car is approaching from behind at a speed of

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supplemented with the constancy of the speed of light, inertial frames of reference transform among themselves according to the

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However, in the Newtonian system the Galilean transformation connects these frames and in the special theory of relativity the

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modifies the distinction between nominally "inertial" and "non-inertial" effects by replacing special relativity's "flat"

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means that inertial frames of reference do not exist globally as they do in Newtonian mechanics and special relativity.

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has external causes. The principle of simplicity can be used within Newtonian physics as well as in special relativity:

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will remain at rest and a body in motion will continue to move uniformly—that is, in a straight line and at constant

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apart. Since neither of the cars is accelerating, we can determine their positions by the following formulas, where

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The presence of fictitious forces indicates the physical laws are not the simplest laws available, in terms of the

3275: 3093:. Given a point of interest that exists in both frames, the vector from the inertial origin to the point is called 3014:

To illustrate further, consider the question: "Does the Universe rotate?" An answer might explain the shape of the

2950: 2555: 2326:-direction. Assuming Candace's acceleration is constant, what acceleration does Betsy measure? If Betsy's velocity 1633: 1502: 1453: 899:

vary depending on the acceleration of that frame with respect to an inertial frame. Viewed from the perspective of

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Absolute space acts on physical objects by inducing their resistance to acceleration but it cannot be acted upon.

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Newton posited an absolute space considered well-approximated by a frame of reference stationary relative to the

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galaxy using the laws of physics, although other observations might be more definitive; that is, provide larger

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of objects in one inertial frame can be converted to measurements in another by a simple transformation — the

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The Principle of Relativity: a collection of original memoirs on the special and general theory of relativity

851:. However, this is not required for the definition, and it is now known that those stars are in fact moving. 5029: 4554: 3063: 3039: 3023: 2862:

pointing in the direction of the axis of rotation, and with magnitude equal to the angular rate of rotation

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that requires no external input, and therefore cannot be jammed by any external or internal signal source.

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of the body according to a rotating observer (different from the velocity seen by the inertial observer).

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generalizes the notion of an inertial frame to include all physical laws, not simply Newton's first law.

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is the relative velocity of the two inertial reference frames. Under Galilean transformations, the time

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of the particle (also a vector) which would be measured by an observer at rest in the frame. The force

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The inadequacy of the notion of "absolute space" in Newtonian mechanics is spelled out by Blagojevich:

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Newton enunciated a principle of relativity himself in one of his corollaries to the laws of motion:

6012: 5951: 5902: 5724: 5700:"Constraints on the proper motion of the Andromeda Galaxy based on the survival of its satellite M33" 4697: 3953:{\displaystyle \mathbf {F} '_{\mathrm {Euler} }=-m{\dot {\boldsymbol {\omega }}}\times \mathbf {r} '} 2867: 1521: 711: 706: 671: 579: 575: 567: 557: 347: 340: 96: 6320: 5937: 5545:

Information Theory and Quantum Physics: Physical Foundations for Understanding the Conscious Process

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are the velocity and acceleration of the accelerated system with respect to the inertial system and

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Wlodzimierz Godlowski; Marek Szydlowski (2003). "Dark energy and global rotation of the Universe".

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First, we could observe the two cars from the side of the road. We define our "frame of reference"

1610: 1550: 1480: 931: 900: 486: 427: 405: 150: 145: 140: 40: 4044:{\displaystyle \mathbf {F} '_{\mathrm {Coriolis} }=-2m{\boldsymbol {\omega }}\times \mathbf {v} '} 2003: 1169: 862:

look the same in all inertial reference frames, and no inertial frame is privileged over another.

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itself and not from any physical force acting on the body. Examples of fictitious forces are the

4353: 4251: 3042:. So far, observations show any rotation of the universe is very slow, no faster than once every 2512: 2497: 2485: 2438: 2419: 1940: 1900: 1629: 1598: 1590: 1027: 971: 967: 920: 908: 904: 879: 828: 817: 801: 616: 357: 232: 200: 160: 4892:

Lange, Ludwig (1885). "Über die wissenschaftliche Fassung des Galileischen Beharrungsgesetzes".

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An example of a new type of cosmological solutions of Einstein's field equations of gravitation

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are the velocity and acceleration of the point of interest with respect to the inertial frame.

2376:-direction—a smaller value than Alfred has measured. Similarly, if she is accelerating at rate 1656:: Two cars moving at different but constant velocities observed from stationary inertial frame 6239: 6233: 6218: 6174: 6108: 6083: 6039: 5863: 5834: 5807: 5780: 5699: 5678: 5620: 5609: 5590: 5579: 5560: 5549: 5522: 5495: 5444: 5414: 5410: 5383: 5373: 5348: 5320: 5257: 5230: 5186: 5159: 5129: 5100: 5074: 5064: 5008: 4981: 4954: 4922: 4848: 4821: 4770: 4743: 4705: 4691: 4670: 4656: 4630: 4626: 4591: 4519: 4390:, Newton expressed the idea of undetectability of straight-line accelerations held in common: 4286:

Inertial and non-inertial reference frames can be distinguished by the absence or presence of

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about their center of gravity, and the example of the curvature of the surface of water in a

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However, the general theory reduces to the special theory over sufficiently small regions of

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connects them. The two transformations agree for speeds of translation much less than the

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are a subgroup. In Newtonian mechanics, inertial frames of reference are related by the

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These equations allow transformations between the two coordinate systems; for example,

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effects are important, there are additional conceptual complications that arise in

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The invariance of the speed of light leads to counter-intuitive phenomena, such as

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in 1885, to replace Newton's definitions of "absolute space and time" with a more

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For example, there is no body providing a gravitational or electrical attraction.

5603: 5573: 5543: 5314: 5180: 4451: 4440: 3961: 3035: 2942: 2908: 2520:. Schwarzschild pointed out that that was invariably seen: the direction of the 1468: 1066: 863: 848: 4264: 6377: 6364: 6315: 5914: 2923:. Also, fictitious forces do not drop off with distance (unlike, for example, 2619: 1606: 1388: 1371:

between two simultaneous events (or, equivalently, the length of any object, |

481: 155: 17: 5387: 5078: 1549:

historically long-lived view that the distant universe might affect matters (

4428: 3015: 2983: 2504: 832: 503: 6293: 6284: 6304:

Effect of the Global Rotation of the Universe on the Formation of Galaxies

2219: 1026:

However, this definition of inertial frames is understood to apply in the

827:

All frames of reference with zero acceleration are in a state of constant

5897: 5719: 2889: 2254: 1368: 836: 422: 305: 280: 6268: 6007: 4693:

Einstein's Space-Time: An Introduction to Special and General Relativity

4314:, a frame where fictitious forces are present is not an inertial frame: 3337:{\displaystyle \mathbf {F} =m\mathbf {a} =m\mathbf {A} +m\mathbf {a} '.} 2541:, is satisfied: Any free motion has a constant magnitude and direction. 1513:. Newtonian inertial frames transform among each other according to the 6391: 5253:

Six not-so-easy pieces: Einstein's relativity, symmetry, and space-time

4817:

Six not-so-easy pieces: Einstein's relativity, symmetry, and space-time

4634: 1449: 951: 947: 916: 821: 395: 248: 165: 5370:

Special relativity and classical field theory: the theoretical minimum

2982:

As now known, the fixed stars are not fixed. Those that reside in the

5963: 5698:

Abraham Loeb; Mark J. Reid; Andreas Brunthaler; Heino Falcke (2005).

3156:

Taking the first and second derivatives of this with respect to time

2920: 2386:-direction (speeding up), she will observe Candace's acceleration as 895:

has non-zero acceleration. In such a frame, the interactions between

454: 300: 210: 6288:

On physical foundations and observational effects of cosmic rotation

3097:, and the vector from the accelerated origin to the point is called 1883:{\displaystyle x_{1}(t)=d+v_{1}t=200+22t,\quad x_{2}(t)=v_{2}t=30t.} 5736: 3352:

direction, or in a direction orthogonal to an object's motion, the

2858:

where the angular rotation of the frame is expressed by the vector

1467:; as a practical matter, "absolute space" was considered to be the 5347:(4th Revised English ed.). Pergamon Press. pp. 273–274. 5063:(Second ed.). Oxford UK: Oxford University Press. p. 1. 4349: 4274: 3050:

years (10 rad/yr), and debate persists over whether there is

2945:

were invoked as a reference frame, supposedly at rest relative to

1510: 1498: 939: 290: 285: 227: 6265:

Rom. Journ. Phys., Vol. 53, Nos. 1–2, P. 405–415, Bucharest, 2008

1452:

frame of reference, or inertial reference frame, is one in which

6263:

Modeling the electric and magnetic fields in a rotating universe

2691:

which looks the same as in an inertial frame, but now the force

2295:-direction. If she is driving north, then north is the positive 1367:

between two events is the same for all reference frames and the

911:

caused by the interaction of objects have to be supplemented by

843:

holds. Such frames are known as inertial. Some physicists, like

295: 258: 4582:

Discovering the Natural Laws: The Experimental Basis of Physics

2457:

General relativity is based upon the principle of equivalence:

954:. Nevertheless, for many applications the Earth is an adequate 4445: 6080:

Fundamentals of High Accuracy Inertial Navigation, Volume 174

4941:

L. Lange (1885) as quoted by Max von Laue in his book (1921)

6177:(1900). "La théorie de Lorentz et le Principe de Réaction". 6107:(pbk. ed.). Hoboken: Taylor & Francis. p. 95. 3512:

or, to solve for the acceleration in the accelerated frame,

1493:

Hence, with respect to an inertial frame, an object or body

1298: 1234: 1202: 5641:

Section 3: The Work of Karl Schwarzschild (2.2 MB PDF-file)

5465:

On the influence of gravitation on the propagation of light

4696:, Springer Science & Business Media, pp. 209–210, 2911:. These terms all have these properties: they vanish when 1436:

has an arbitrary but fixed rotation with respect to frame

923:, the fictitious (i.e. inertial) forces are attributed to 6214:

Mach's Principle: From Newton's Bucket to Quantum Gravity

5120:

Robert Resnick; David Halliday; Kenneth S. Krane (2001).

2301:-direction; if she turns east, east becomes the positive 2277:-axis, and the direction in front of her as the positive 2241:-axis, and the direction in front of him as the positive 934:, its surface is not an inertial frame of reference. The 88:{\displaystyle {\textbf {F}}={\frac {d\mathbf {p} }{dt}}} 5440:

Physics for Scientists and Engineers with Modern Physics

3245:{\displaystyle \mathbf {a} =\mathbf {A} +\mathbf {a} '.} 3198:{\displaystyle \mathbf {v} =\mathbf {V} +\mathbf {v} ',} 3146:{\displaystyle \mathbf {r} =\mathbf {R} +\mathbf {r} '.} 2470:

Physics for Scientists and Engineers with Modern Physics

1395:: Two frames of reference moving with relative velocity 5319:(reprinted ed.). Courier Corporation. p. 27. 4921: ed.). Oxford University Press. pp. 645–646. 2154:. To catch up to the first car, it will take a time of 4235:

Separating non-inertial from inertial reference frames

2626:, electromagnetic, gravitational, and nuclear forces. 1349:

represent shifts in the origin of space and time, and

5518:

No Easy Answers: Science and the Pursuit of Knowledge

4063: 3972: 3886: 3671: 3521: 3375: 3287: 3212: 3165: 3113: 2708: 2650: 2558: 2406:-direction—a larger value than Alfred's measurement. 2081: 2048: 2006: 1983: 1943: 1903: 1772: 1729: 1689: 1401: 1292: 1226: 1194: 1172: 820:. Observed relative to such a frame, objects exhibit 52: 2344:-direction. However, if she is accelerating at rate 2133:

Alternatively, we could choose a frame of reference

1613:, the transformation between inertial frames is the 1479:

is abandoned, and an inertial frame in the field of

1217:, by simple addition or subtraction of coordinates: 835:acting on it, is perceived to move with a constant 6390:from the original on 13 November 2021 – via 5402: 5121: 4618: 4579: 4218: 4043: 3952: 3866: 3647: 3501: 3336: 3244: 3197: 3145: 2847: 2680: 2583: 2122: 2066: 2033: 1989: 1969: 1929: 1882: 1751: 1711: 1424: 1324: 1275: 1209: 1180: 992:The foundation of the general theory of relativity 87: 5091:For a discussion of the role of fixed stars, see 5036:. Metaphysics Research Lab, Stanford University. 938:can deflect certain forms of motion as seen from 6269:Yuri N. Obukhov, Thoralf Chrobok, Mike Scherfner 6168:Relativity, the special and the general theories 5605:Cosmological Inflation and Large-Scale Structure 4406:Corollary VI, p. 89, in Andrew Motte translation 1719:is the position in meters of car one after time 1571:, Corollary V, p. 88 in Andrew Motte translation 5491:Physics Through the Nineteen Nineties: Overview 4617:Sidney Borowitz; Lawrence A. Bornstein (1968). 4392: 4316: 4292: 2459: 1660:attached to the road and moving inertial frame 1558: 1527: 1485: 1137: 1104: 1094: 1005: 980: 5521:. University of Pittsburgh Press. p. 66. 2681:{\displaystyle \mathbf {F} '=m\mathbf {a} \ ,} 2622:of all "real" forces on the particle, such as 2584:{\displaystyle \mathbf {F} =m\mathbf {a} \ ,} 777: 8: 6342:Rev. Mod. Phys., Vol. 21, p. 447, 1949. 5275: 5273: 5128:(5th ed.). Wiley. Volume 1, Chapter 3. 4301:Sidney Borowitz and Lawrence A Bornstein in 3362:This arrangement leads to the equation (see 1505:), in the absence of a net force, a body at 1448:Within the realm of Newtonian mechanics, an 6211:Julian B. Barbour; Herbert Pfister (1998). 6035:Mathematical Methods of Classical Mechanics 5608:. Cambridge University Press. p. 329. 5158:. New Delhi: Tata McGraw-Hill. p. 70. 4880:rotating sphere Mach cord OR string OR rod. 4669:. Courier Dover Publications. p. 111. 4480:. Unsourced material may be challenged and 4332:Mathematical Methods of Classical Mechanics 3055:along the geodesics in general relativity. 1520:If this rule is interpreted as saying that 1049: 5862:. Imperial College Press. p. 32, §9. 5632:In the Shadow of the Relativity Revolution 5602:Liddle, Andrew R.; Lyth, David H. (2000). 4793:Relativity: The Special and General Theory 4612: 4610: 2226:: Simple-minded frame-of-reference example 1471:In the theory of relativity the notion of 1038:of symmetry transformations, of which the 784: 770: 31: 27:Fundamental concept of classical mechanics 6353:Stanford Encyclopedia of Philosophy entry 6129:"The gyroscope pilots ships & planes" 6103:Kennie, T.J.M.; Petrie, G., eds. (1993). 6006: 5896: 5718: 5212:. Princeton University Press. p. 58. 4621:A Contemporary View of Elementary Physics 4573: 4571: 4500:Learn how and when to remove this message 4352:that result from the acceleration of the 4303:A Contemporary View of Elementary Physics 4208: 4196: 4187: 4172: 4165: 4140: 4131: 4120: 4071: 4070: 4065: 4062: 4032: 4023: 3980: 3979: 3974: 3971: 3941: 3926: 3925: 3894: 3893: 3888: 3885: 3855: 3850: 3803: 3802: 3797: 3762: 3761: 3756: 3730: 3729: 3724: 3692: 3691: 3686: 3673: 3670: 3636: 3631: 3615: 3606: 3595: 3583: 3574: 3559: 3544: 3543: 3535: 3523: 3520: 3490: 3485: 3469: 3460: 3449: 3437: 3428: 3413: 3398: 3397: 3385: 3376: 3374: 3322: 3310: 3299: 3288: 3286: 3230: 3221: 3213: 3211: 3183: 3174: 3166: 3164: 3131: 3122: 3114: 3112: 2833: 2828: 2808: 2802: 2787: 2782: 2773: 2762: 2750: 2745: 2736: 2722: 2710: 2707: 2667: 2652: 2649: 2570: 2559: 2557: 2123:{\displaystyle t=25\ \mathrm {seconds} .} 2094: 2080: 2047: 2005: 1982: 1961: 1948: 1942: 1921: 1908: 1902: 1859: 1837: 1805: 1777: 1771: 1734: 1728: 1694: 1688: 1408: 1407: 1405: 1403: 1402: 1400: 1316: 1297: 1291: 1265: 1256: 1251: 1242: 1233: 1228: 1225: 1201: 1196: 1193: 1173: 1171: 69: 63: 54: 53: 51: 5494:. National Academies Press. p. 15. 5368:Susskind, Leonard; Art Friedman (2017). 4950:A Modern Approach to Classical Mechanics 4874:. The Open Court Publishing Co. p. 4263: 2934:All observers agree on the real forces, 2218: 1648: 1425:{\displaystyle {\stackrel {\vec {v}}{}}} 1387: 1030:realm and ignores relativistic effects. 6194:On the Electrodynamics of Moving Bodies 5651:Landau, L. D.; Lifshitz, E. M. (1960). 5488:National Research Council (US) (1986). 5316:Relativity for Scientists and Engineers 5223:William Geraint Vaughan Rosser (1991). 5096:Nothingness: The Science of Empty Space 5034:The Stanford Encyclopedia of Philosophy 4567: 4209: 4188: 4132: 4121: 4024: 3928: 3607: 3596: 3575: 3546: 3461: 3450: 3429: 3400: 2525:approximately Galilean or Minkowskian. 2247:-axis. To him, the car moves along the 103: 39: 6238:. Springer. p. 369; Footnote 12. 5443:. Pearson Prentice Hall. p. 155. 5409:. Cambridge University Press. p. 5185:. London/Berlin: Springer. p. 6. 4841:Armin Wachter; Henning Hoeber (2006). 4586:. Courier Dover Publications. p. 2629:In contrast, Newton's second law in a 1893:Notice that these formulas predict at 1759:is the position of car two after time 1621:which is used in Newtonian mechanics. 1210:{\displaystyle \mathbf {s} ^{\prime }} 970:. According to the first postulate of 816:) is a stationary or uniformly moving 5997:Gilson, James G. (1 September 2004), 5372:. New York: Hachette UK. Figure 2.1. 466:Newton's law of universal gravitation 7: 6333:Nature 298, 451 – 454 (29 July 1982) 6306:General Relativity and Gravitation, 5800:Peter Graneau; Neal Graneau (2006). 5578:. Academic Publishers. p. 116. 4478:adding citations to reliable sources 1050:Newton's inertial frame of reference 5803:In the Grip of the Distant Universe 5754:from the original on 11 August 2017 5405:Introduction to Classical Mechanics 5155:Introduction to classical mechanics 5040:from the original on 7 January 2016 4742:. Hackett Publishing. p. 212. 3104:From the geometry of the situation 3004:collision course with the Milky Way 1325:{\displaystyle t^{\prime }=t-t_{0}} 447:Mechanics of planar particle motion 55: 5885:General Relativity and Gravitation 5572:Bandyopadhyay, Nikhilendu (2000). 4102: 4099: 4096: 4093: 4090: 4087: 4084: 4081: 4078: 4075: 4072: 4002: 3999: 3996: 3993: 3990: 3987: 3984: 3981: 3907: 3904: 3901: 3898: 3895: 3834: 3831: 3828: 3825: 3822: 3819: 3816: 3813: 3810: 3807: 3804: 3784: 3781: 3778: 3775: 3772: 3769: 3766: 3763: 3743: 3740: 3737: 3734: 3731: 3714: 3711: 3708: 3705: 3702: 3699: 3696: 3693: 2443:Introduction to general relativity 2113: 2110: 2107: 2104: 2101: 2098: 2095: 919:. Viewed from the perspective of 25: 5978:from the original on 5 March 2016 5806:. World Scientific. p. 147. 5250:Richard Phillips Feynman (1998). 5030:"Space and Time: Inertial Frames" 4953:. World Scientific. p. 169. 4844:Compendium of Theoretical Physics 4814:Richard Phillips Feynman (1998). 4718:from the original on 7 March 2023 4348:forces (pseudo-forces); that is, 2986:turn with the galaxy, exhibiting 878:(combined with a translation) in 6135:. 15 March 1943. pp. 80–83. 6105:Engineering Surveying Technology 5478:, vol. 35, (1911) : 898–908 5007:. London: Springer. p. 58. 4977:Gravitation and Gauge Symmetries 4766:Gravitation and Gauge Symmetries 4450: 4197: 4173: 4141: 4066: 4033: 3975: 3942: 3889: 3851: 3798: 3757: 3725: 3687: 3674: 3658:Multiplying through by the mass 3632: 3616: 3584: 3560: 3536: 3524: 3486: 3470: 3438: 3414: 3386: 3377: 3323: 3311: 3300: 3289: 3231: 3222: 3214: 3184: 3175: 3167: 3132: 3123: 3115: 2974:. In both cases, application of 2829: 2809: 2783: 2774: 2763: 2746: 2737: 2723: 2711: 2668: 2653: 2571: 2560: 1576:This principle differs from the 1266: 1252: 1243: 1229: 1197: 1174: 1162:Classical theories that use the 1127:Gravitation and Gauge Symmetries 1019:Gravitation and Gauge Symmetries 958:of an inertial reference frame. 751: 750: 737: 70: 6281:Phys. Rev. D 66, 043518 (2002) 5660:. Pergamon Press. pp. 4–6. 5343:LD Landau; LM Lifshitz (1975). 5226:Introductory Special Relativity 4796:. H. Holt and Company. p. 4312:special principle of relativity 2695:′ is the resultant of not only 2641:about an axis, takes the form: 2635:non-inertial frame of reference 1832: 1458:principle of special relativity 1150:Space and Time: Inertial Frames 856:principle of special relativity 5858:. In J. M. T. Thompson (ed.). 5833:. Da Capo Press. p. 275. 5779:. Springer. pp. 235–236. 5345:The Classical Theory of Fields 5099:. Da Capo Press. p. 150. 5028:Robert DiSalle (Summer 2002). 4416:accelerates at the same rate. 4311: 4213: 4205: 4184: 4158: 4149: 4128: 3624: 3603: 3478: 3457: 3028:microwave background radiation 2793: 2770: 1849: 1843: 1789: 1783: 1746: 1740: 1706: 1700: 1577: 1457: 1413: 1: 6279:Shear-free rotating inflation 6160:, 2nd ed. (Freeman, NY, 1992) 6078:Chatfield, Averil B. (1997). 5425:acceleration azimuthal Morin. 4342:non-inertial reference frames 3026:, like the anisotropy of the 2895:The extra terms in the force 373:Koopman–von Neumann mechanics 5575:Theory of Special Relativity 5437:Douglas C. Giancoli (2007). 5032:. In Edward N. Zalta (ed.). 4919:Absolute or Relative Motion? 4802:The Principle of Relativity. 2879:locates the body and vector 2637:), rotating at angular rate 2529:Inertial frames and rotation 2034:{\displaystyle 200+22t=30t,} 1599:theory of special relativity 1525:was summarized by Einstein: 1515:Galilean group of symmetries 1503:Newton's first law of motion 1454:Newton's first law of motion 1181:{\displaystyle \mathbf {s} } 925:geodesic motion in spacetime 892:non-inertial reference frame 841:Newton's first law of motion 441:Non-inertial reference frame 6217:. Birkhäuser. p. 445. 6198:The Principle of Relativity 5938:"Is the Universe rotating?" 5856:"The Paradigm of Inflation" 5256:. Basic Books. p. 50. 4974:Milutin Blagojević (2002). 4945:, p. 34, and translated by 4820:. Basic Books. p. 73. 4763:Milutin Blagojević (2002). 4425:Inertial navigation systems 3011:about the galactic center. 2631:rotating frame of reference 2606:the mass of a particle and 2424:Rotating frame of reference 1970:{\displaystyle x_{1}=x_{2}} 1930:{\displaystyle x_{1}=x_{2}} 1501:is applied, and (following 1074:inertial frame of reference 806:inertial frame of reference 368:Appell's equation of motion 238:Inertial frame of reference 6440: 5936:Birch, P. (29 July 1982). 5542:Green, Herbert S. (2000). 4911:Julian B. Barbour (2001). 4847:. Birkhäuser. p. 98. 4602:reference laws of physics. 4578:Milton A. Rothman (1989). 4249: 4243: 3038:is invoked to explain the 2446: 2436: 2413: 1664:attached to the first car. 1634:relativity of simultaneity 1588: 1058: 946:will reduce the effective 6378:"Is Gravity An Illusion?" 6331:Is the Universe rotating? 6038:. Springer. p. 129. 5854:J Garcio-Bellido (2005). 5707:The Astrophysical Journal 5674:The Music of the Big Bang 5548:. Springer. p. 154. 5209:The Meaning of Relativity 4914:The Discovery of Dynamics 4366:rotating reference frames 4344:are subject to so-called 2992:expansion of the universe 1540:The Meaning of Relativity 921:general relativity theory 6205:Rotation of the Universe 5776:Einstein from "B" to "Z" 5773:John J. Stachel (2002). 5677:. Springer. p. 59. 5470:24 December 2020 at the 5285:Andrew Motte Translation 5229:. CRC Press. p. 3. 5061:The Theory of Relativity 4980:. CRC Press. p. 5. 4871:The Science of Mechanics 4790:Albert Einstein (1920). 4769:. CRC Press. p. 4. 4739:The Structure of Science 4690:Ferraro, Rafael (2007), 3064:quantum reference frames 3032:Big Bang nucleosynthesis 1752:{\displaystyle x_{2}(t)} 1712:{\displaystyle x_{1}(t)} 814:Galilean reference frame 531:Rotating reference frame 363:Hamilton–Jacobi equation 6358:4 December 2010 at the 6316:10.1023/A:1018867011142 5915:10.1023/A:1027301723533 5515:Allan Franklin (2007). 4943:Die Relativitätstheorie 4625:. McGraw-Hill. p. 4555:Quantum reference frame 3040:galactic rotation curve 3024:measurement uncertainty 2951:Newton's laws of motion 2866:, symbol × denotes the 2067:{\displaystyle 8t=200,} 1619:Galilean transformation 1456:is valid. However, the 1164:Galilean transformation 1061:Absolute space and time 1040:Lorentz transformations 868:Galilean transformation 472:Newton's laws of motion 332:Newton's laws of motion 6179:Archives Neerlandaises 6154:John Archibald Wheeler 5297:Lorentz transformation 5179:NMJ Woodhouse (2003). 5001:NMJ Woodhouse (2003). 4894:Philosophische Studien 4409: 4338: 4335:Second Edition, p. 129 4308: 4283: 4272: 4220: 4045: 3954: 3868: 3649: 3503: 3338: 3246: 3199: 3147: 2849: 2682: 2585: 2533:In an inertial frame, 2475: 2227: 2124: 2068: 2035: 1991: 1971: 1931: 1884: 1753: 1713: 1665: 1615:Lorentz transformation 1574: 1546: 1491: 1445: 1426: 1326: 1277: 1211: 1182: 1155: 1132: 1100: 1090:operational definition 1081: 1024: 997: 876:Lorentz transformation 499:Simple harmonic motion 412:Euler's laws of motion 206:D'Alembert's principle 89: 6253:B Ciobanu, I Radinchi 6200:, page 38. Dover 1923 5860:Advances in Astronomy 5827:Henning Genz (2001). 5671:Amedeo Balbi (2008). 5313:Skinner, Ray (2014). 5093:Henning Genz (2001). 4736:Ernest Nagel (1979). 4540:Local reference frame 4278: 4267: 4221: 4046: 3955: 3869: 3650: 3504: 3339: 3247: 3200: 3148: 2941:In Newton's time the 2850: 2683: 2586: 2468:Douglas C. Giancoli, 2449:Equivalence principle 2222: 2125: 2069: 2036: 1992: 1972: 1932: 1885: 1754: 1714: 1652: 1497:only when a physical 1427: 1391: 1385:|) is also the same. 1327: 1278: 1212: 1183: 353:Hamiltonian mechanics 171:Statistical mechanics 90: 6419:Theory of relativity 6326:5 March 2016 at the 6258:19 July 2013 at the 5401:David Morin (2008). 4474:improve this section 4061: 3970: 3884: 3669: 3519: 3373: 3285: 3210: 3163: 3111: 2998:. For instance, the 2994:, and partly due to 2968:two spheres rotating 2907:, and the third the 2868:vector cross product 2706: 2648: 2556: 2079: 2046: 2004: 1981: 1941: 1937:. Therefore, we set 1901: 1770: 1727: 1687: 1522:straight-line motion 1399: 1290: 1224: 1192: 1170: 1125:Milutin Blagojević: 1017:Milutin Blagojević: 839:, or, equivalently, 576:Angular acceleration 568:Rotational frequency 348:Lagrangian mechanics 341:Analytical mechanics 97:Second law of motion 50: 6414:Frames of reference 6409:Classical mechanics 6299:9 July 2017 at the 6274:9 July 2017 at the 6017:2004physics...9010G 5999:Mach's Principle II 5956:1982Natur.298..451B 5907:2003GReGr..35.2171G 5729:2005ApJ...633..894L 5637:20 May 2017 at the 5621:Extract of page 329 5591:Extract of page 116 5561:Extract of page 154 5206:A Einstein (1950). 5152:RG Takwale (1980). 4947:Harald Iro (2002). 4868:Ernst Mach (1915). 4702:2007esti.book.....F 4530:Galilean invariance 4388:linear acceleration 4110: 4010: 3915: 3842: 3792: 3751: 3366:for a derivation): 3276:Newton's second law 2996:peculiar velocities 2976:Newton's second law 2958:, for example, the 2543:Newton's second law 2410:Non-inertial frames 2314:and finds it to be 1481:classical mechanics 1158:Newtonian mechanics 1001:non-inertial frames 968:frames of reference 901:classical mechanics 428:Harmonic oscillator 406:Equations of motion 41:Classical mechanics 35:Part of a series on 6068:a different frame. 5476:Annalen der Physik 5332:Extract of page 27 5182:Special relativity 5004:Special relativity 4550:Newton's first law 4545:Lorentz covariance 4535:General covariance 4427:used a cluster of 4284: 4273: 4252:Non-inertial frame 4216: 4064: 4041: 3973: 3950: 3887: 3864: 3796: 3755: 3723: 3645: 3499: 3334: 3278:can be written as 3242: 3195: 3143: 2845: 2678: 2581: 2535:Newton's first law 2513:Karl Schwarzschild 2498:geodesic deviation 2439:General relativity 2433:General relativity 2420:Non-inertial frame 2228: 2215:Additional example 2120: 2064: 2031: 1987: 1967: 1927: 1880: 1749: 1709: 1666: 1630:length contraction 1591:Special relativity 1585:Special relativity 1446: 1422: 1322: 1273: 1207: 1178: 972:special relativity 905:special relativity 880:special relativity 829:rectilinear motion 818:frame of reference 802:special relativity 744:Physics portal 358:Routhian mechanics 233:Frame of reference 85: 6232:PJ Nahin (1999). 6170:, 15th ed. (1954) 6158:Spacetime Physics 6045:978-0-387-96890-2 5950:(5873): 451–454. 5891:(12): 2171–2187. 5684:978-3-540-78726-6 5528:978-0-8229-5968-7 5450:978-0-13-149508-1 5420:978-0-521-87622-3 5379:978-0-465-09334-2 5354:978-0-7506-2768-9 5326:978-0-486-79367-2 5059:C Møller (1976). 4917:(Reprint of 1989 4520:Absolute rotation 4510: 4509: 4502: 4358:centrifugal force 4288:fictitious forces 4228:centrifugal force 3934: 3552: 3406: 2964:centrifugal force 2956:fictitious forces 2929:electrical forces 2905:centrifugal force 2903:, the second the 2841: 2822: 2674: 2598:the net force (a 2577: 2511:: The astronomer 2479:Eötvös experiment 2453:Eötvös experiment 2093: 1990:{\displaystyle t} 1578:special principle 1537:Albert Einstein: 1419: 1416: 990:Albert Einstein: 944:centrifugal force 913:fictitious forces 872:Newtonian physics 854:According to the 798:classical physics 794: 793: 541:Centrifugal force 536:Centripetal force 492:Euler's equations 477:Relative velocity 253:Moment of inertia 83: 57: 16:(Redirected from 6431: 6395: 6367: 6249: 6228: 6186: 6137: 6136: 6125: 6119: 6118: 6100: 6094: 6093: 6075: 6069: 6065: 6059: 6056: 6050: 6049: 6026: 6020: 6019: 6010: 5994: 5988: 5987: 5985: 5983: 5964:10.1038/298451a0 5933: 5927: 5926: 5900: 5898:astro-ph/0303248 5880: 5874: 5873: 5851: 5845: 5844: 5824: 5818: 5817: 5797: 5791: 5790: 5770: 5764: 5763: 5761: 5759: 5753: 5722: 5720:astro-ph/0506609 5704: 5695: 5689: 5688: 5668: 5662: 5661: 5659: 5648: 5642: 5629: 5623: 5619: 5599: 5593: 5589: 5569: 5563: 5559: 5539: 5533: 5532: 5512: 5506: 5505: 5485: 5479: 5461: 5455: 5454: 5434: 5428: 5427: 5408: 5398: 5392: 5391: 5365: 5359: 5358: 5340: 5334: 5330: 5310: 5304: 5293: 5287: 5277: 5268: 5267: 5247: 5241: 5240: 5220: 5214: 5213: 5203: 5197: 5196: 5176: 5170: 5169: 5149: 5143: 5142: 5140:physics resnick. 5127: 5117: 5111: 5110: 5089: 5083: 5082: 5056: 5050: 5049: 5047: 5045: 5025: 5019: 5018: 4998: 4992: 4991: 4971: 4965: 4964: 4939: 4933: 4932: 4908: 4902: 4901: 4889: 4883: 4882: 4865: 4859: 4858: 4838: 4832: 4831: 4811: 4805: 4804: 4787: 4781: 4780: 4760: 4754: 4753: 4733: 4727: 4726: 4725: 4723: 4687: 4681: 4680: 4645: 4639: 4638: 4624: 4614: 4605: 4604: 4585: 4575: 4505: 4498: 4494: 4491: 4485: 4454: 4446: 4407: 4336: 4306: 4256:Rotating spheres 4246:Fictitious force 4225: 4223: 4222: 4217: 4212: 4204: 4200: 4191: 4180: 4176: 4170: 4169: 4148: 4144: 4135: 4124: 4106: 4105: 4069: 4050: 4048: 4047: 4042: 4040: 4036: 4027: 4006: 4005: 3978: 3959: 3957: 3956: 3951: 3949: 3945: 3936: 3935: 3927: 3911: 3910: 3892: 3873: 3871: 3870: 3865: 3860: 3859: 3854: 3838: 3837: 3801: 3788: 3787: 3760: 3747: 3746: 3728: 3719: 3718: 3717: 3690: 3681: 3677: 3654: 3652: 3651: 3646: 3641: 3640: 3635: 3623: 3619: 3610: 3599: 3591: 3587: 3578: 3567: 3563: 3554: 3553: 3545: 3539: 3531: 3527: 3508: 3506: 3505: 3500: 3495: 3494: 3489: 3477: 3473: 3464: 3453: 3445: 3441: 3432: 3421: 3417: 3408: 3407: 3399: 3393: 3389: 3380: 3364:Fictitious force 3343: 3341: 3340: 3335: 3330: 3326: 3314: 3303: 3292: 3251: 3249: 3248: 3243: 3238: 3234: 3225: 3217: 3204: 3202: 3201: 3196: 3191: 3187: 3178: 3170: 3152: 3150: 3149: 3144: 3139: 3135: 3126: 3118: 3049: 3047: 3000:Andromeda Galaxy 2854: 2852: 2851: 2846: 2839: 2838: 2837: 2832: 2823: 2821: 2813: 2812: 2803: 2792: 2791: 2786: 2777: 2766: 2755: 2754: 2749: 2740: 2726: 2718: 2714: 2687: 2685: 2684: 2679: 2672: 2671: 2660: 2656: 2590: 2588: 2587: 2582: 2575: 2574: 2563: 2549:takes the form: 2522:angular momentum 2509:Milky Way galaxy 2473: 2416:Fictitious force 2405: 2400:in the negative 2399: 2385: 2380:in the positive 2375: 2370:in the negative 2369: 2355: 2350:in the negative 2349: 2343: 2338:in the negative 2337: 2331: 2325: 2320:in the negative 2319: 2306: 2300: 2294: 2289:in the negative 2288: 2282: 2276: 2267: 2262:in the positive 2261: 2252: 2246: 2240: 2206: 2202: 2200: 2198: 2197: 2194: 2191: 2184: 2182: 2181: 2166: 2163: 2153: 2129: 2127: 2126: 2121: 2116: 2091: 2073: 2071: 2070: 2065: 2040: 2038: 2037: 2032: 1996: 1994: 1993: 1988: 1976: 1974: 1973: 1968: 1966: 1965: 1953: 1952: 1936: 1934: 1933: 1928: 1926: 1925: 1913: 1912: 1889: 1887: 1886: 1881: 1864: 1863: 1842: 1841: 1810: 1809: 1782: 1781: 1758: 1756: 1755: 1750: 1739: 1738: 1718: 1716: 1715: 1710: 1699: 1698: 1682: 1572: 1551:Mach's principle 1544: 1477:privileged frame 1440:. They are both 1431: 1429: 1428: 1423: 1421: 1420: 1418: 1417: 1409: 1406: 1404: 1331: 1329: 1328: 1323: 1321: 1320: 1302: 1301: 1282: 1280: 1279: 1274: 1269: 1261: 1260: 1255: 1246: 1238: 1237: 1232: 1216: 1214: 1213: 1208: 1206: 1205: 1200: 1187: 1185: 1184: 1179: 1177: 1153: 1130: 1084:) was coined by 1022: 995: 932:Earth's rotation 897:physical objects 786: 779: 772: 759: 754: 753: 746: 742: 741: 647:Johann Bernoulli 642:Daniel Bernoulli 563:Tangential speed 467: 443: 418:Fictitious force 413: 265:Mechanical power 255: 196:Angular momentum 94: 92: 91: 86: 84: 82: 74: 73: 64: 59: 58: 32: 21: 6439: 6438: 6434: 6433: 6432: 6430: 6429: 6428: 6399: 6398: 6386:. 3 June 2015. 6376: 6365: 6360:Wayback Machine 6349: 6328:Wayback Machine 6301:Wayback Machine 6285:Yuri N. Obukhov 6276:Wayback Machine 6260:Wayback Machine 6246: 6231: 6225: 6210: 6190:Albert Einstein 6175:Poincaré, Henri 6173: 6164:Albert Einstein 6150:Edwin F. Taylor 6146: 6144:Further reading 6141: 6140: 6127: 6126: 6122: 6115: 6102: 6101: 6097: 6090: 6077: 6076: 6072: 6066: 6062: 6057: 6053: 6046: 6028: 6027: 6023: 6008:physics/0409010 5996: 5995: 5991: 5981: 5979: 5935: 5934: 5930: 5882: 5881: 5877: 5870: 5853: 5852: 5848: 5841: 5826: 5825: 5821: 5814: 5799: 5798: 5794: 5787: 5772: 5771: 5767: 5757: 5755: 5751: 5702: 5697: 5696: 5692: 5685: 5670: 5669: 5665: 5657: 5650: 5649: 5645: 5639:Wayback Machine 5630: 5626: 5616: 5601: 5600: 5596: 5586: 5571: 5570: 5566: 5556: 5541: 5540: 5536: 5529: 5514: 5513: 5509: 5502: 5487: 5486: 5482: 5472:Wayback Machine 5462: 5458: 5451: 5436: 5435: 5431: 5421: 5400: 5399: 5395: 5380: 5367: 5366: 5362: 5355: 5342: 5341: 5337: 5327: 5312: 5311: 5307: 5294: 5290: 5278: 5271: 5264: 5249: 5248: 5244: 5237: 5222: 5221: 5217: 5205: 5204: 5200: 5193: 5178: 5177: 5173: 5166: 5151: 5150: 5146: 5136: 5119: 5118: 5114: 5107: 5092: 5090: 5086: 5071: 5058: 5057: 5053: 5043: 5041: 5027: 5026: 5022: 5015: 5000: 4999: 4995: 4988: 4973: 4972: 4968: 4961: 4946: 4940: 4936: 4929: 4910: 4909: 4905: 4891: 4890: 4886: 4867: 4866: 4862: 4855: 4840: 4839: 4835: 4828: 4813: 4812: 4808: 4789: 4788: 4784: 4777: 4762: 4761: 4757: 4750: 4735: 4734: 4730: 4721: 4719: 4712: 4689: 4688: 4684: 4677: 4647: 4646: 4642: 4616: 4615: 4608: 4598: 4577: 4576: 4569: 4564: 4559: 4515: 4506: 4495: 4489: 4486: 4471: 4455: 4422: 4408: 4401: 4354:reference frame 4337: 4325: 4307: 4300: 4262: 4260:Bucket argument 4248: 4242: 4237: 4195: 4171: 4161: 4139: 4059: 4058: 4031: 3968: 3967: 3940: 3882: 3881: 3849: 3685: 3672: 3667: 3666: 3630: 3614: 3582: 3558: 3522: 3517: 3516: 3484: 3468: 3436: 3412: 3384: 3371: 3370: 3354:Coriolis effect 3321: 3283: 3282: 3229: 3208: 3207: 3182: 3161: 3160: 3130: 3109: 3108: 3072: 3045: 3043: 2972:rotating bucket 2887: 2878: 2827: 2814: 2804: 2781: 2744: 2709: 2704: 2703: 2651: 2646: 2645: 2554: 2553: 2531: 2494:geodesic motion 2490:Minkowski Space 2474: 2467: 2455: 2445: 2437:Main articles: 2435: 2426: 2414:Main articles: 2412: 2401: 2387: 2381: 2371: 2357: 2351: 2345: 2339: 2333: 2327: 2321: 2315: 2302: 2296: 2290: 2284: 2278: 2272: 2263: 2257: 2253:axis with some 2248: 2242: 2236: 2217: 2204: 2195: 2192: 2189: 2188: 2186: 2180: 2173: 2167: 2164: 2159: 2158: 2156: 2155: 2151: 2144: 2138: 2077: 2076: 2044: 2043: 2002: 2001: 1979: 1978: 1957: 1944: 1939: 1938: 1917: 1904: 1899: 1898: 1855: 1833: 1801: 1773: 1768: 1767: 1730: 1725: 1724: 1723:in seconds and 1690: 1685: 1684: 1677: 1647: 1642: 1593: 1587: 1581:further below. 1573: 1566: 1545: 1536: 1483:is defined as: 1442:inertial frames 1397: 1396: 1384: 1377: 1366: 1359: 1348: 1341: 1312: 1293: 1288: 1287: 1250: 1227: 1222: 1221: 1195: 1190: 1189: 1168: 1167: 1160: 1154: 1148:Robert DiSalle 1146: 1131: 1124: 1072:The expression 1063: 1057: 1052: 1046:of symmetries. 1023: 1016: 1010: 996: 994:, Section A, §1 989: 964: 936:Coriolis effect 909:physical forces 889:By contrast, a 790: 749: 736: 735: 728: 727: 726: 601: 593: 592: 572: 526:Circular motion 520: 510: 509: 508: 465: 435: 432: 411: 390: 382: 381: 378: 377: 335: 325: 317: 316: 315: 274: 270:Mechanical work 263: 247: 185: 177: 176: 175: 130: 122: 99: 75: 65: 48: 47: 28: 23: 22: 15: 12: 11: 5: 6437: 6435: 6427: 6426: 6421: 6416: 6411: 6401: 6400: 6397: 6396: 6383:PBS Space Time 6374: 6366:Animation clip 6362: 6348: 6347:External links 6345: 6344: 6343: 6334: 6318: 6291: 6282: 6266: 6250: 6244: 6229: 6223: 6207: 6206: 6202: 6201: 6196:, included in 6187: 6171: 6161: 6145: 6142: 6139: 6138: 6120: 6113: 6095: 6088: 6070: 6060: 6051: 6044: 6021: 5989: 5928: 5875: 5868: 5846: 5839: 5819: 5812: 5792: 5785: 5765: 5737:10.1086/491644 5713:(2): 894–898. 5690: 5683: 5663: 5643: 5624: 5614: 5594: 5584: 5564: 5554: 5534: 5527: 5507: 5500: 5480: 5463:A. Einstein, " 5456: 5449: 5429: 5419: 5393: 5378: 5360: 5353: 5335: 5325: 5305: 5301:speed of light 5288: 5269: 5262: 5242: 5235: 5215: 5198: 5191: 5171: 5164: 5144: 5134: 5112: 5105: 5084: 5069: 5051: 5020: 5013: 4993: 4986: 4966: 4959: 4934: 4927: 4903: 4884: 4860: 4853: 4833: 4826: 4806: 4782: 4775: 4755: 4748: 4728: 4710: 4682: 4675: 4653:Lorentz, H. A. 4640: 4606: 4596: 4566: 4565: 4563: 4560: 4558: 4557: 4552: 4547: 4542: 4537: 4532: 4527: 4525:Diffeomorphism 4522: 4516: 4514: 4511: 4508: 4507: 4458: 4456: 4449: 4434:dead reckoning 4421: 4418: 4402:Isaac Newton: 4399: 4377:force carriers 4362:Coriolis force 4323: 4298: 4244:Main article: 4241: 4238: 4236: 4233: 4232: 4231: 4215: 4211: 4207: 4203: 4199: 4194: 4190: 4186: 4183: 4179: 4175: 4168: 4164: 4160: 4157: 4154: 4151: 4147: 4143: 4138: 4134: 4130: 4127: 4123: 4119: 4116: 4113: 4109: 4104: 4101: 4098: 4095: 4092: 4089: 4086: 4083: 4080: 4077: 4074: 4068: 4056: 4053:Coriolis force 4039: 4035: 4030: 4026: 4022: 4019: 4016: 4013: 4009: 4004: 4001: 3998: 3995: 3992: 3989: 3986: 3983: 3977: 3965: 3948: 3944: 3939: 3933: 3930: 3924: 3921: 3918: 3914: 3909: 3906: 3903: 3900: 3897: 3891: 3875: 3874: 3863: 3858: 3853: 3848: 3845: 3841: 3836: 3833: 3830: 3827: 3824: 3821: 3818: 3815: 3812: 3809: 3806: 3800: 3795: 3791: 3786: 3783: 3780: 3777: 3774: 3771: 3768: 3765: 3759: 3754: 3750: 3745: 3742: 3739: 3736: 3733: 3727: 3722: 3716: 3713: 3710: 3707: 3704: 3701: 3698: 3695: 3689: 3684: 3680: 3676: 3656: 3655: 3644: 3639: 3634: 3629: 3626: 3622: 3618: 3613: 3609: 3605: 3602: 3598: 3594: 3590: 3586: 3581: 3577: 3573: 3570: 3566: 3562: 3557: 3551: 3548: 3542: 3538: 3534: 3530: 3526: 3510: 3509: 3498: 3493: 3488: 3483: 3480: 3476: 3472: 3467: 3463: 3459: 3456: 3452: 3448: 3444: 3440: 3435: 3431: 3427: 3424: 3420: 3416: 3411: 3405: 3402: 3396: 3392: 3388: 3383: 3379: 3345: 3344: 3333: 3329: 3325: 3320: 3317: 3313: 3309: 3306: 3302: 3298: 3295: 3291: 3253: 3252: 3241: 3237: 3233: 3228: 3224: 3220: 3216: 3205: 3194: 3190: 3186: 3181: 3177: 3173: 3169: 3154: 3153: 3142: 3138: 3134: 3129: 3125: 3121: 3117: 3071: 3068: 2988:proper motions 2960:Coriolis force 2947:absolute space 2925:nuclear forces 2901:Coriolis force 2883: 2874: 2856: 2855: 2844: 2836: 2831: 2826: 2820: 2817: 2811: 2807: 2801: 2798: 2795: 2790: 2785: 2780: 2776: 2772: 2769: 2765: 2761: 2758: 2753: 2748: 2743: 2739: 2735: 2732: 2729: 2725: 2721: 2717: 2713: 2689: 2688: 2677: 2670: 2666: 2663: 2659: 2655: 2624:contact forces 2592: 2591: 2580: 2573: 2569: 2566: 2562: 2539:law of inertia 2530: 2527: 2486:general theory 2465: 2434: 2431: 2411: 2408: 2216: 2213: 2178: 2171: 2149: 2142: 2131: 2130: 2119: 2115: 2112: 2109: 2106: 2103: 2100: 2097: 2090: 2087: 2084: 2074: 2063: 2060: 2057: 2054: 2051: 2041: 2030: 2027: 2024: 2021: 2018: 2015: 2012: 2009: 1986: 1977:and solve for 1964: 1960: 1956: 1951: 1947: 1924: 1920: 1916: 1911: 1907: 1891: 1890: 1879: 1876: 1873: 1870: 1867: 1862: 1858: 1854: 1851: 1848: 1845: 1840: 1836: 1831: 1828: 1825: 1822: 1819: 1816: 1813: 1808: 1804: 1800: 1797: 1794: 1791: 1788: 1785: 1780: 1776: 1748: 1745: 1742: 1737: 1733: 1708: 1705: 1702: 1697: 1693: 1646: 1645:Simple example 1643: 1641: 1638: 1603:speed of light 1589:Main article: 1586: 1583: 1567:Isaac Newton: 1564: 1534: 1473:absolute space 1465:absolute space 1415: 1412: 1382: 1375: 1364: 1357: 1346: 1339: 1333: 1332: 1319: 1315: 1311: 1308: 1305: 1300: 1296: 1284: 1283: 1272: 1268: 1264: 1259: 1254: 1249: 1245: 1241: 1236: 1231: 1204: 1199: 1188:, to another, 1176: 1159: 1156: 1144: 1122: 1116: 1115: 1112: 1109: 1082:Inertialsystem 1059:Main article: 1056: 1055:Absolute space 1053: 1051: 1048: 1044:Galilean group 1036:Poincaré group 1014: 987: 963: 960: 884:speed of light 810:inertial space 792: 791: 789: 788: 781: 774: 766: 763: 762: 761: 760: 747: 730: 729: 725: 724: 719: 714: 709: 704: 699: 694: 689: 684: 679: 674: 669: 664: 659: 654: 649: 644: 639: 634: 629: 624: 619: 614: 609: 603: 602: 599: 598: 595: 594: 591: 590: 571: 570: 565: 560: 555: 553:Coriolis force 550: 549: 548: 538: 533: 528: 522: 521: 516: 515: 512: 511: 507: 506: 501: 496: 495: 494: 489: 479: 474: 469: 462: 451: 450: 449: 444: 431: 430: 425: 420: 415: 408: 403: 398: 392: 391: 388: 387: 384: 383: 380: 379: 376: 375: 370: 365: 360: 355: 350: 344: 338: 336: 329: 326: 323: 322: 319: 318: 314: 313: 308: 303: 298: 293: 288: 283: 278: 272: 267: 261: 256: 245: 240: 235: 230: 225: 224: 223: 218: 208: 203: 198: 193: 187: 186: 183: 182: 179: 178: 174: 173: 168: 163: 158: 153: 148: 143: 138: 132: 131: 128: 127: 124: 123: 121: 120: 115: 110: 104: 101: 100: 95: 81: 78: 72: 68: 62: 44: 43: 37: 36: 26: 24: 18:Inertial space 14: 13: 10: 9: 6: 4: 3: 2: 6436: 6425: 6422: 6420: 6417: 6415: 6412: 6410: 6407: 6406: 6404: 6393: 6389: 6385: 6384: 6379: 6375: 6372: 6368: 6363: 6361: 6357: 6354: 6351: 6350: 6346: 6341: 6338: 6335: 6332: 6329: 6325: 6322: 6319: 6317: 6313: 6309: 6305: 6302: 6298: 6295: 6292: 6289: 6286: 6283: 6280: 6277: 6273: 6270: 6267: 6264: 6261: 6257: 6254: 6251: 6247: 6245:0-387-98571-9 6241: 6237: 6236: 6235:Time Machines 6230: 6226: 6224:0-8176-3823-7 6220: 6216: 6215: 6209: 6208: 6204: 6203: 6199: 6195: 6191: 6188: 6184: 6180: 6176: 6172: 6169: 6165: 6162: 6159: 6155: 6151: 6148: 6147: 6143: 6134: 6130: 6124: 6121: 6116: 6114:9780203860748 6110: 6106: 6099: 6096: 6091: 6089:9781600864278 6085: 6081: 6074: 6071: 6064: 6061: 6055: 6052: 6047: 6041: 6037: 6036: 6031: 6030:V. I. Arnol'd 6025: 6022: 6018: 6014: 6009: 6004: 6000: 5993: 5990: 5977: 5973: 5969: 5965: 5961: 5957: 5953: 5949: 5945: 5944: 5939: 5932: 5929: 5924: 5920: 5916: 5912: 5908: 5904: 5899: 5894: 5890: 5886: 5879: 5876: 5871: 5869:1-86094-577-5 5865: 5861: 5857: 5850: 5847: 5842: 5840:0-7382-0610-5 5836: 5832: 5831: 5823: 5820: 5815: 5813:981-256-754-2 5809: 5805: 5804: 5796: 5793: 5788: 5786:0-8176-4143-2 5782: 5778: 5777: 5769: 5766: 5750: 5746: 5742: 5738: 5734: 5730: 5726: 5721: 5716: 5712: 5708: 5701: 5694: 5691: 5686: 5680: 5676: 5675: 5667: 5664: 5656: 5655: 5647: 5644: 5640: 5636: 5633: 5628: 5625: 5622: 5617: 5615:0-521-57598-2 5611: 5607: 5606: 5598: 5595: 5592: 5587: 5581: 5577: 5576: 5568: 5565: 5562: 5557: 5551: 5547: 5546: 5538: 5535: 5530: 5524: 5520: 5519: 5511: 5508: 5503: 5501:0-309-03579-1 5497: 5493: 5492: 5484: 5481: 5477: 5473: 5469: 5466: 5460: 5457: 5452: 5446: 5442: 5441: 5433: 5430: 5426: 5422: 5416: 5412: 5407: 5406: 5397: 5394: 5389: 5385: 5381: 5375: 5371: 5364: 5361: 5356: 5350: 5346: 5339: 5336: 5333: 5328: 5322: 5318: 5317: 5309: 5306: 5302: 5298: 5292: 5289: 5286: 5282: 5276: 5274: 5270: 5265: 5263:0-201-32842-9 5259: 5255: 5254: 5246: 5243: 5238: 5236:0-85066-838-7 5232: 5228: 5227: 5219: 5216: 5211: 5210: 5202: 5199: 5194: 5192:1-85233-426-6 5188: 5184: 5183: 5175: 5172: 5167: 5165:0-07-096617-6 5161: 5157: 5156: 5148: 5145: 5141: 5137: 5135:0-471-32057-9 5131: 5126: 5125: 5116: 5113: 5108: 5106:0-7382-0610-5 5102: 5098: 5097: 5088: 5085: 5080: 5076: 5072: 5070:0-19-560539-X 5066: 5062: 5055: 5052: 5039: 5035: 5031: 5024: 5021: 5016: 5014:1-85233-426-6 5010: 5006: 5005: 4997: 4994: 4989: 4987:0-7503-0767-6 4983: 4979: 4978: 4970: 4967: 4962: 4960:981-238-213-5 4956: 4952: 4951: 4944: 4938: 4935: 4930: 4928:0-19-513202-5 4924: 4920: 4916: 4915: 4907: 4904: 4899: 4895: 4888: 4885: 4881: 4877: 4873: 4872: 4864: 4861: 4856: 4854:0-387-25799-3 4850: 4846: 4845: 4837: 4834: 4829: 4827:0-201-32842-9 4823: 4819: 4818: 4810: 4807: 4803: 4799: 4795: 4794: 4786: 4783: 4778: 4776:0-7503-0767-6 4772: 4768: 4767: 4759: 4756: 4751: 4749:0-915144-71-9 4745: 4741: 4740: 4732: 4729: 4717: 4713: 4711:9780387699462 4707: 4703: 4699: 4695: 4694: 4686: 4683: 4678: 4676:0-486-60081-5 4672: 4668: 4667: 4662: 4658: 4657:Minkowski, H. 4654: 4650: 4644: 4641: 4636: 4632: 4628: 4623: 4622: 4613: 4611: 4607: 4603: 4599: 4597:0-486-26178-6 4593: 4589: 4584: 4583: 4574: 4572: 4568: 4561: 4556: 4553: 4551: 4548: 4546: 4543: 4541: 4538: 4536: 4533: 4531: 4528: 4526: 4523: 4521: 4518: 4517: 4512: 4504: 4501: 4493: 4483: 4479: 4475: 4469: 4468: 4464: 4459:This section 4457: 4453: 4448: 4447: 4444: 4442: 4437: 4435: 4430: 4426: 4419: 4417: 4413: 4405: 4398: 4397: 4391: 4389: 4384: 4380: 4378: 4372: 4369: 4367: 4363: 4359: 4355: 4351: 4347: 4343: 4334: 4333: 4328: 4327:V. 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Arnol'd 4322: 4321: 4315: 4313: 4304: 4297: 4296: 4291: 4289: 4281: 4277: 4270: 4266: 4261: 4257: 4253: 4247: 4239: 4234: 4229: 4201: 4192: 4181: 4177: 4166: 4162: 4155: 4152: 4145: 4136: 4125: 4117: 4114: 4111: 4107: 4057: 4054: 4037: 4028: 4020: 4017: 4014: 4011: 4007: 3966: 3963: 3946: 3937: 3931: 3922: 3919: 3916: 3912: 3880: 3879: 3878: 3861: 3856: 3846: 3843: 3839: 3793: 3789: 3752: 3748: 3720: 3682: 3678: 3665: 3664: 3663: 3661: 3642: 3637: 3627: 3620: 3611: 3600: 3592: 3588: 3579: 3571: 3568: 3564: 3555: 3549: 3540: 3532: 3528: 3515: 3514: 3513: 3496: 3491: 3481: 3474: 3465: 3454: 3446: 3442: 3433: 3425: 3422: 3418: 3409: 3403: 3394: 3390: 3381: 3369: 3368: 3367: 3365: 3360: 3357: 3355: 3351: 3331: 3327: 3318: 3315: 3307: 3304: 3296: 3293: 3281: 3280: 3279: 3277: 3272: 3270: 3266: 3262: 3258: 3239: 3235: 3226: 3218: 3206: 3192: 3188: 3179: 3171: 3159: 3158: 3157: 3140: 3136: 3127: 3119: 3107: 3106: 3105: 3102: 3100: 3096: 3092: 3087: 3085: 3081: 3077: 3070:Primed frames 3069: 3067: 3065: 3061: 3056: 3053: 3041: 3037: 3033: 3029: 3025: 3021: 3020:discrepancies 3017: 3012: 3008: 3005: 3001: 2997: 2993: 2989: 2985: 2980: 2977: 2973: 2969: 2965: 2961: 2957: 2952: 2948: 2944: 2939: 2937: 2932: 2930: 2926: 2922: 2918: 2914: 2910: 2906: 2902: 2898: 2893: 2891: 2886: 2882: 2877: 2873: 2869: 2865: 2861: 2842: 2834: 2824: 2818: 2815: 2805: 2799: 2796: 2788: 2778: 2767: 2759: 2756: 2751: 2741: 2733: 2730: 2727: 2719: 2715: 2702: 2701: 2700: 2698: 2694: 2675: 2664: 2661: 2657: 2644: 2643: 2642: 2640: 2636: 2632: 2627: 2625: 2621: 2617: 2613: 2609: 2605: 2601: 2597: 2578: 2567: 2564: 2552: 2551: 2550: 2548: 2544: 2540: 2536: 2528: 2526: 2523: 2519: 2514: 2510: 2506: 2501: 2499: 2495: 2491: 2487: 2482: 2480: 2471: 2464: 2463: 2458: 2454: 2450: 2444: 2440: 2432: 2430: 2425: 2421: 2417: 2409: 2407: 2404: 2398: 2394: 2390: 2384: 2379: 2374: 2368: 2364: 2360: 2354: 2348: 2342: 2336: 2330: 2324: 2318: 2313: 2308: 2305: 2299: 2293: 2287: 2281: 2275: 2269: 2266: 2260: 2256: 2251: 2245: 2239: 2232: 2225: 2221: 2214: 2212: 2208: 2177: 2170: 2162: 2148: 2141: 2136: 2117: 2088: 2085: 2082: 2075: 2061: 2058: 2055: 2052: 2049: 2042: 2028: 2025: 2022: 2019: 2016: 2013: 2010: 2007: 2000: 1999: 1998: 1984: 1962: 1958: 1954: 1949: 1945: 1922: 1918: 1914: 1909: 1905: 1896: 1877: 1874: 1871: 1868: 1865: 1860: 1856: 1852: 1846: 1838: 1834: 1829: 1826: 1823: 1820: 1817: 1814: 1811: 1806: 1802: 1798: 1795: 1792: 1786: 1778: 1774: 1766: 1765: 1764: 1762: 1743: 1735: 1731: 1722: 1703: 1695: 1691: 1680: 1675: 1670: 1663: 1659: 1655: 1651: 1644: 1639: 1637: 1635: 1631: 1627: 1626:time dilation 1622: 1620: 1616: 1612: 1608: 1604: 1600: 1597: 1592: 1584: 1582: 1579: 1570: 1563: 1562: 1557: 1554: 1552: 1542: 1541: 1533: 1532: 1531:acceleration. 1526: 1523: 1518: 1516: 1512: 1508: 1504: 1500: 1496: 1490: 1489: 1484: 1482: 1478: 1474: 1470: 1466: 1461: 1459: 1455: 1451: 1443: 1439: 1435: 1410: 1394: 1390: 1386: 1381: 1374: 1370: 1363: 1356: 1352: 1345: 1338: 1317: 1313: 1309: 1306: 1303: 1294: 1286: 1285: 1270: 1262: 1257: 1247: 1239: 1220: 1219: 1218: 1165: 1157: 1152: 1151: 1143: 1142: 1136: 1128: 1121: 1120: 1117: 1113: 1110: 1107: 1106: 1103: 1099: 1098: 1093: 1091: 1087: 1083: 1079: 1075: 1070: 1068: 1062: 1054: 1047: 1045: 1041: 1037: 1031: 1029: 1020: 1013: 1012: 1004: 1002: 993: 986: 985: 979: 977: 973: 969: 961: 959: 957: 956:approximation 953: 949: 945: 941: 937: 933: 928: 926: 922: 918: 914: 910: 906: 902: 898: 894: 893: 887: 885: 881: 877: 873: 869: 865: 861: 860:physical laws 857: 852: 850: 846: 842: 838: 834: 830: 825: 823: 819: 815: 811: 808:(also called 807: 803: 799: 787: 782: 780: 775: 773: 768: 767: 765: 764: 758: 748: 745: 740: 734: 733: 732: 731: 723: 720: 718: 715: 713: 710: 708: 705: 703: 700: 698: 695: 693: 690: 688: 685: 683: 680: 678: 675: 673: 670: 668: 665: 663: 660: 658: 655: 653: 650: 648: 645: 643: 640: 638: 635: 633: 630: 628: 625: 623: 620: 618: 615: 613: 610: 608: 605: 604: 597: 596: 589: 585: 581: 577: 574: 573: 569: 566: 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Retrieved 5947: 5941: 5931: 5888: 5884: 5878: 5859: 5849: 5829: 5822: 5802: 5795: 5775: 5768: 5756:. Retrieved 5710: 5706: 5693: 5673: 5666: 5653: 5646: 5627: 5604: 5597: 5574: 5567: 5544: 5537: 5517: 5510: 5490: 5483: 5475: 5459: 5439: 5432: 5424: 5404: 5396: 5369: 5363: 5344: 5338: 5315: 5308: 5291: 5280: 5252: 5245: 5225: 5218: 5208: 5201: 5181: 5174: 5154: 5147: 5139: 5123: 5115: 5095: 5087: 5060: 5054: 5042:. Retrieved 5033: 5023: 5003: 4996: 4976: 4969: 4949: 4942: 4937: 4918: 4913: 4906: 4897: 4893: 4887: 4879: 4870: 4863: 4843: 4836: 4816: 4809: 4801: 4792: 4785: 4765: 4758: 4738: 4731: 4720:, retrieved 4692: 4685: 4665: 4649:Einstein, A. 4643: 4620: 4601: 4581: 4496: 4487: 4472:Please help 4460: 4438: 4423: 4420:Applications 4414: 4410: 4403: 4394: 4393: 4385: 4381: 4373: 4370: 4345: 4339: 4330: 4318: 4317: 4309: 4302: 4294: 4293: 4285: 4279: 4268: 3876: 3659: 3657: 3511: 3361: 3358: 3346: 3273: 3268: 3264: 3260: 3256: 3254: 3155: 3103: 3098: 3094: 3090: 3088: 3083: 3079: 3075: 3073: 3057: 3051: 3013: 3009: 2981: 2940: 2935: 2933: 2916: 2912: 2896: 2894: 2884: 2880: 2875: 2871: 2863: 2859: 2857: 2696: 2692: 2690: 2638: 2634: 2628: 2615: 2612:acceleration 2607: 2603: 2595: 2593: 2538: 2532: 2518:Solar System 2502: 2483: 2476: 2469: 2461: 2460: 2456: 2427: 2402: 2396: 2392: 2388: 2382: 2377: 2372: 2366: 2362: 2358: 2352: 2346: 2340: 2334: 2328: 2322: 2316: 2312:acceleration 2309: 2307:-direction. 2303: 2297: 2291: 2285: 2279: 2273: 2270: 2264: 2258: 2249: 2243: 2237: 2233: 2229: 2223: 2209: 2175: 2168: 2160: 2146: 2139: 2134: 2132: 1894: 1892: 1760: 1720: 1678: 1673: 1671: 1667: 1661: 1657: 1653: 1623: 1594: 1575: 1568: 1560: 1559: 1555: 1547: 1538: 1529: 1528: 1519: 1492: 1487: 1486: 1462: 1447: 1441: 1437: 1433: 1392: 1379: 1372: 1361: 1354: 1350: 1343: 1336: 1334: 1161: 1149: 1139: 1138: 1133: 1126: 1119: 1118: 1105: 1101: 1096: 1095: 1086:Ludwig Lange 1073: 1071: 1064: 1032: 1025: 1018: 1007: 1006: 1000: 998: 991: 982: 981: 965: 962:Introduction 929: 907:, the usual 890: 888: 864:Measurements 853: 845:Isaac Newton 826: 813: 809: 805: 795: 586: / 582: / 580:displacement 578: / 439: / 436: 401:Displacement 339: 330: 324:Formulations 311:Virtual work 251: / 237: 191:Acceleration 184:Fundamentals 29: 5982:14 December 5830:Nothingness 5758:15 December 5283:on line at 5044:9 September 4441:gyrocompass 3962:Euler force 3350:centrifugal 3036:dark matter 2943:fixed stars 2909:Euler force 2484:Einstein's 1997:, that is: 1495:accelerates 1469:fixed stars 1067:fixed stars 976:translation 849:fixed stars 722:von Neumann 389:Core topics 6403:Categories 6337:Kurt Gödel 5585:8186358528 5555:354066517X 4722:2 November 4635:B000GQB02A 4562:References 4429:gyroscopes 4346:fictitious 4340:Bodies in 4250:See also: 2620:vector sum 2447:See also: 1632:, and the 1617:, not the 1607:free space 1596:Einstein's 942:, and the 915:caused by 657:d'Alembert 637:Maupertuis 600:Scientists 482:Rigid body 156:Kinematics 6294:Li-Xin Li 6185:: 253–78. 5923:118988129 5654:Mechanics 5388:968771417 5281:Principia 5079:220221617 4490:July 2013 4461:does not 4404:Principia 4210:ω 4193:⋅ 4189:ω 4182:− 4163:ω 4137:× 4133:ω 4126:× 4122:ω 4115:− 4029:× 4025:ω 4015:− 3938:× 3932:˙ 3929:ω 3920:− 3844:− 3628:− 3612:× 3608:ω 3601:× 3597:ω 3593:− 3580:× 3576:ω 3569:− 3556:× 3550:˙ 3547:ω 3541:− 3466:× 3462:ω 3455:× 3451:ω 3434:× 3430:ω 3410:× 3404:˙ 3401:ω 3016:Milky Way 2984:Milky Way 2870:, vector 2825:× 2810:Ω 2797:− 2779:× 2775:Ω 2768:× 2764:Ω 2757:− 2742:× 2738:Ω 2728:− 2505:spacetime 2472:, p. 155. 1611:invariant 1569:Principia 1414:→ 1310:− 1299:′ 1263:− 1248:− 1235:′ 1203:′ 1028:Newtonian 833:net force 702:Liouville 584:frequency 504:Vibration 221:potential 146:Continuum 141:Celestial 118:Textbooks 6388:Archived 6356:Archived 6324:Archived 6297:Archived 6272:Archived 6256:Archived 6082:. AIAA. 6032:(1989). 5976:Archived 5749:Archived 5745:17099715 5635:Archived 5468:Archived 5279:See the 5038:Archived 4716:archived 4663:(1952). 4661:Weyl, H. 4513:See also 4400:— 4360:and the 4324:— 4305:, p. 138 4299:— 4280:Figure 3 4269:Figure 2 4202:′ 4178:′ 4146:′ 4108:′ 4038:′ 4008:′ 3947:′ 3913:′ 3840:′ 3790:′ 3749:′ 3679:′ 3621:′ 3589:′ 3565:′ 3529:′ 3475:′ 3443:′ 3419:′ 3391:′ 3328:′ 3236:′ 3189:′ 3137:′ 3022:or less 2962:and the 2890:velocity 2716:′ 2658:′ 2547:particle 2466:— 2255:velocity 2224:Figure 2 1654:Figure 1 1640:Examples 1565:— 1535:— 1450:inertial 1432:. Frame 1393:Figure 1 1369:distance 1145:— 1123:— 1015:— 988:— 837:velocity 757:Category 682:Hamilton 667:Lagrange 662:Clairaut 627:Horrocks 588:velocity 558:Pendulum 546:reactive 518:Rotation 487:dynamics 437:Inertial 423:Friction 306:Velocity 281:Momentum 161:Kinetics 151:Dynamics 129:Branches 113:Timeline 6392:YouTube 6371:YouTube 6321:P Birch 6310:(1998) 6013:Bibcode 5972:4343095 5952:Bibcode 5903:Bibcode 5725:Bibcode 5124:Physics 4698:Bibcode 4482:removed 4467:sources 4396:forces. 4320:system. 3060:quantum 2888:is the 2618:is the 2199:⁠ 2187:⁠ 2183:⁠ 2157:⁠ 2152:= 8 m/s 1681:= 200 m 1543:, p. 58 952:equator 950:at the 948:gravity 930:Due to 917:inertia 874:or the 822:inertia 717:Koopman 677:Poisson 672:Laplace 617:Huygens 612:Galileo 457: ( 396:Damping 249:Inertia 243:Impulse 216:kinetic 166:Statics 136:Applied 108:History 6424:Orbits 6290:(2000) 6242: 6221: 6111: 6086: 6042: 5970: 5943:Nature 5921: 5866: 5837: 5810: 5783: 5743: 5681: 5612: 5582: 5552: 5525: 5498: 5447: 5417: 5386: 5376: 5351: 5323: 5260: 5233: 5189: 5162: 5132: 5103: 5077: 5067: 5011: 4984: 4957: 4925: 4851: 4824: 4773: 4746: 4708: 4673: 4633: 4594: 4350:forces 4258:, and 4240:Theory 3877:where 3662:gives 3255:where 3002:is on 2921:matter 2840: 2673: 2600:vector 2576: 2545:for a 2537:, the 2422:, and 2092: 1335:where 1129:, p. 5 1078:German 1021:, p. 4 858:, all 755: 707:Appell 692:Cauchy 687:Jacobi 632:Halley 622:Newton 607:Kepler 459:linear 455:Motion 301:Torque 276:Moment 211:Energy 201:Couple 6003:arXiv 5968:S2CID 5919:S2CID 5893:arXiv 5752:(PDF) 5741:S2CID 5715:arXiv 5703:(PDF) 5658:(PDF) 4588:23-24 3058:When 2594:with 2205:8 m/s 1511:speed 1499:force 1475:or a 1141:them. 940:Earth 812:, or 804:, an 712:Gibbs 697:Routh 652:Euler 291:Speed 286:Space 228:Force 6240:ISBN 6219:ISBN 6152:and 6133:Life 6109:ISBN 6084:ISBN 6040:ISBN 5984:2008 5864:ISBN 5835:ISBN 5808:ISBN 5781:ISBN 5760:2008 5679:ISBN 5610:ISBN 5580:ISBN 5550:ISBN 5523:ISBN 5496:ISBN 5445:ISBN 5415:ISBN 5384:OCLC 5374:ISBN 5349:ISBN 5321:ISBN 5258:ISBN 5231:ISBN 5187:ISBN 5160:ISBN 5130:ISBN 5101:ISBN 5075:OCLC 5065:ISBN 5046:2008 5009:ISBN 4982:ISBN 4955:ISBN 4923:ISBN 4849:ISBN 4822:ISBN 4771:ISBN 4744:ISBN 4724:2022 4706:ISBN 4671:ISBN 4631:ASIN 4592:ISBN 4465:any 4463:cite 4386:For 3267:and 3259:and 2610:the 2451:and 2441:and 1507:rest 1342:and 903:and 800:and 296:Time 259:Mass 6369:on 6312:doi 5960:doi 5948:298 5911:doi 5733:doi 5711:633 5474:", 5411:649 4627:138 4476:by 4364:in 4290:. 3356:). 3052:any 3030:or 2927:or 2633:(a 2602:), 2190:200 2059:200 2008:200 1818:200 1609:is 1605:in 1434:S' 1092:: 870:in 796:In 6405:: 6380:. 6308:30 6192:, 6181:. 6166:, 6156:, 6131:. 6011:, 6001:, 5974:. 5966:. 5958:. 5946:. 5940:. 5917:. 5909:. 5901:. 5889:35 5887:. 5747:. 5739:. 5731:. 5723:. 5709:. 5705:. 5423:. 5413:. 5382:. 5272:^ 5138:. 5073:. 4896:. 4878:. 4876:38 4800:. 4798:17 4714:, 4704:, 4659:; 4655:; 4651:; 4629:. 4609:^ 4600:. 4590:. 4570:^ 4439:A 4368:. 4329:: 4254:, 4230:). 4055:), 3964:), 3101:. 3099:r′ 3086:. 3084:a′ 3082:, 3080:y′ 3078:, 3076:x′ 3066:. 3048:10 2418:, 2395:+ 2391:= 2389:a′ 2365:− 2361:= 2359:a′ 2207:. 2185:= 2174:− 2145:− 2135:S′ 2089:25 2023:30 2014:22 1872:30 1824:22 1763:. 1662:S′ 1628:, 1517:. 1378:− 1360:− 1080:: 984:K. 927:. 886:. 6394:. 6314:: 6248:. 6227:. 6183:V 6117:. 6092:. 6048:. 6015:: 6005:: 5986:. 5962:: 5954:: 5925:. 5913:: 5905:: 5895:: 5872:. 5843:. 5816:. 5789:. 5762:. 5735:: 5727:: 5717:: 5687:. 5618:. 5588:. 5558:. 5531:. 5504:. 5453:. 5390:. 5357:. 5329:. 5303:. 5266:. 5239:. 5195:. 5168:. 5109:. 5081:. 5048:. 5017:. 4990:. 4963:. 4931:. 4900:. 4898:2 4857:. 4830:. 4779:. 4752:. 4700:: 4679:. 4637:. 4503:) 4497:( 4492:) 4488:( 4484:. 4470:. 4226:( 4214:) 4206:) 4198:r 4185:( 4174:r 4167:2 4159:( 4156:m 4153:= 4150:) 4142:r 4129:( 4118:m 4112:= 4103:l 4100:a 4097:g 4094:u 4091:f 4088:i 4085:r 4082:t 4079:n 4076:e 4073:c 4067:F 4051:( 4034:v 4021:m 4018:2 4012:= 4003:s 4000:i 3997:l 3994:o 3991:i 3988:r 3985:o 3982:C 3976:F 3960:( 3943:r 3923:m 3917:= 3908:r 3905:e 3902:l 3899:u 3896:E 3890:F 3862:, 3857:0 3852:A 3847:m 3835:l 3832:a 3829:t 3826:e 3823:p 3820:i 3817:r 3814:t 3811:n 3808:e 3805:c 3799:F 3794:+ 3785:s 3782:i 3779:l 3776:o 3773:i 3770:r 3767:o 3764:C 3758:F 3753:+ 3744:r 3741:e 3738:l 3735:u 3732:E 3726:F 3721:+ 3715:l 3712:a 3709:c 3706:i 3703:s 3700:y 3697:h 3694:p 3688:F 3683:= 3675:F 3660:m 3643:. 3638:0 3633:A 3625:) 3617:r 3604:( 3585:v 3572:2 3561:r 3537:a 3533:= 3525:a 3497:, 3492:0 3487:A 3482:+ 3479:) 3471:r 3458:( 3447:+ 3439:v 3426:2 3423:+ 3415:r 3395:+ 3387:a 3382:= 3378:a 3332:. 3324:a 3319:m 3316:+ 3312:A 3308:m 3305:= 3301:a 3297:m 3294:= 3290:F 3269:a 3265:v 3261:A 3257:V 3240:. 3232:a 3227:+ 3223:A 3219:= 3215:a 3193:, 3185:v 3180:+ 3176:V 3172:= 3168:v 3141:. 3133:r 3128:+ 3124:R 3120:= 3116:r 3095:r 3091:R 3046:× 3044:6 2936:F 2917:Ω 2913:Ω 2897:F 2885:B 2881:v 2876:B 2872:x 2864:Ω 2860:Ω 2843:, 2835:B 2830:x 2819:t 2816:d 2806:d 2800:m 2794:) 2789:B 2784:x 2771:( 2760:m 2752:B 2747:v 2734:m 2731:2 2724:F 2720:= 2712:F 2697:F 2693:F 2676:, 2669:a 2665:m 2662:= 2654:F 2639:Ω 2616:F 2608:a 2604:m 2596:F 2579:, 2572:a 2568:m 2565:= 2561:F 2403:y 2397:A 2393:a 2383:y 2378:A 2373:y 2367:A 2363:a 2353:y 2347:A 2341:y 2335:a 2329:v 2323:x 2317:a 2304:y 2298:y 2292:y 2286:v 2280:y 2274:x 2265:x 2259:v 2250:x 2244:y 2238:x 2201:s 2196:8 2193:/ 2179:1 2176:v 2172:2 2169:v 2165:/ 2161:d 2150:1 2147:v 2143:2 2140:v 2118:. 2114:s 2111:d 2108:n 2105:o 2102:c 2099:e 2096:s 2086:= 2083:t 2062:, 2056:= 2053:t 2050:8 2029:, 2026:t 2020:= 2017:t 2011:+ 1985:t 1963:2 1959:x 1955:= 1950:1 1946:x 1923:2 1919:x 1915:= 1910:1 1906:x 1895:t 1878:. 1875:t 1869:= 1866:t 1861:2 1857:v 1853:= 1850:) 1847:t 1844:( 1839:2 1835:x 1830:, 1827:t 1821:+ 1815:= 1812:t 1807:1 1803:v 1799:+ 1796:d 1793:= 1790:) 1787:t 1784:( 1779:1 1775:x 1761:t 1747:) 1744:t 1741:( 1736:2 1732:x 1721:t 1707:) 1704:t 1701:( 1696:1 1692:x 1679:d 1674:S 1658:S 1438:S 1411:v 1383:1 1380:r 1376:2 1373:r 1365:1 1362:t 1358:2 1355:t 1351:v 1347:0 1344:t 1340:0 1337:r 1318:0 1314:t 1307:t 1304:= 1295:t 1271:t 1267:v 1258:0 1253:r 1244:r 1240:= 1230:r 1198:s 1175:s 1076:( 978:: 785:e 778:t 771:v 461:) 80:t 77:d 71:p 67:d 61:= 56:F 20:)

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Knowledge (XXG)

Inertial frame of reference

Index