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Neither view is correct. The Earth and the Sun both revolve around the barycenter (center of mass) of the solar system. In fact, some exoplanets have been discovered due to the motion of the star around its system's barycenter. In special relativity, there is no preferred inertial frame of reference (that is constant velocity frame of reference). But ...

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Inertial Frames of reference are fractals. You can imagine each Frame of reference as a box within a box within a box etc You can zoom in or out. The observer in each inertial "box" see the behavior of matter according to the laws of "classical"Mechanics == That is clocks run normally, mass is constant as is length. Example a car traveling at constant ...

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Let us start from classical physics. The fundamental invariance postulate in classical physics is that all physical laws describing an isolated physical system in an inertial reference frame are invariant in form under the action of Galileian (Lie) group. That group is made of $4$ (Lie) subgroups. (1) spatial translations, invariance under space ...

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There is. Have a look at http://en.wikipedia.org/wiki/Noether%27s_theorem. Isotropie is "coupled" with conservation of angular momentum, homogenity of space to conservation of momentum and homogenity of time to conservation of energy.

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Assume the car is moving in the X direction, let's say to the right. You are inside the car (so you are also moving in the x direction as fast as the car is) and throw the ball in the Y direction, let's say upwards. The motion of the ball, as seen from somebody standing still outside the car, is that of a projectile shot upwards with whatever speed you throw ...

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Explanation When the car accelerates, it accelerates any object bound to it at the same time*: everything in it gains kinetic energy and everything travels at the same speed. When you remove the constraints (by throwing a ball), it still has the speed it has gained from the car acceleration because of inertia. Only exterior forces change the velocity of a ...

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When you tossed the ball inside the car, its initial speed was 100mph, like of all other objects including you and your hand which was holding the ball. Since no force is applied to the ball, it'll keep moving at this speed. It's called inertia.

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The use of inertial frames in Lagrangian mechanics is by no means compulsory and everything can be done in any reference frame provided one takes all forces, real and inertial, into account. Actually there are two possibilities in interpreting the question. We work in a non inertial frame $R'$ (instead of an inertial one $R$) because we are adopting ...

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It depends on how you "derive" Lagrange's equations, whether taking Newton's laws as fundamental or by assuming an action integral and minimizing it. However, there is no such requirement that you be in an inertial frame of reference. Thus, to look at your pendulum problem, you could start with the Lagrangian L = \frac{1}{2} I ...

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I) In e.g. Ref. 1 is shown that there exist (possibly velocity-dependent) generalized potentials for all the fictitious forces, such as, e.g., the centrifugal force, the Coriolis force and the Euler force. So Yes, there exist Lagrangian formulations for non-inertial accelerated reference frames. II) OP's image shows Kapitza's pendulum. Kapitza's pendulum ...

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Actually the COM for the 2-body problem is the essential feature in this subject and with respect to it, both the Earth and the Sun rotate. Indeed, motion is relative, the relativity of it is even easier to understand in the Galilean Relativity than in Special Relativity. The Heliocentric view is actually the correct opinion that the Sun of our planetary ...

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