Geodesic
On the relative movement of equivalent reference systems
Čelâbinskij fiziko-matematičeskij žurnal, Tome 3 (2018) no. 3, pp. 338-343.

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The purpose of the paper is to establish an equation that determines the common element of continuous symmetry of a noninertial rigid reference frame in the classical case. The basis of the analytical method is the generalized principle of relativity of A. A. Logunov. According to this principle, Lagrangians of equivalent reference systems have the same parameters: proper accelerations and angular velocities. This condition severely limits the breadth of the symmetry transformations and allows us to establish a differential equation for the motion of an equivalent reference system with respect to the original system. The general form of the equations solution depends on the solution of the Darboux problem.
Keywords: the generalized principle of relativity, equivalent reference systems, the Darboux problem. 
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V. V. Voitik; N. G. Migranov. On the relative movement of equivalent reference systems. Čelâbinskij fiziko-matematičeskij žurnal, Tome 3 (2018) no. 3, pp. 338-343. http://geodesic.mathdoc.fr/item/CHFMJ_2018_3_3_a6/

[1] Logunov A.A., Lectures on the theory of relativity and gravitation: contemporary analysis of the problem, Nauka Publ., Moscow, 1987, 272 pp. (In Russ.)

[2] Landau L.D., Lifshitz E.M., Course of Theoretical Physics, v. 1, Mechanics, Butterworth-Heinemann, Oxford, 1976, 171 pp. | MR | MR

[3] Lur'ye A.I., Analytical Mechanics, Moscow, 1961 (In Russ.)

[4] Zubov V.I, Ermolin V.S., Igolkin V.N., Kovrigin A.B., Martynenko I.A., Tikhomirov B.P., Dynamics of a free rigid body and determination of its orientation in space, Leningrad State University Publishing, Leningrad, 1968, 208 pp. (In Russ.)

[5] P. Tsiotras, J. M. Longuski, “New kinematic relations for the large angle problem in rigid body attitude dynamics”, Acta Astronautica, 32:3 (1994), 181–190 | DOI | MR