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Dynamics in spaces of constant curvature. (English. Russian original) Zbl 1066.83511
Mosc. Univ. Math. Bull. 49, No. 2, 21-28 (1994); translation from Vestn. Mosk. Univ., Ser. I 1994, No. 2, 28-35 (1994).
From the text: The author studies the problem of motion of a charged particle in the Einstein space-time. The electrostatic field is regarded as external. The metric of the Einstein space-time has the form \[ ds^2 = c^2dt^2 - R^2(d\Theta^2 + \sin^2\Theta(d\varphi^2 + \sin^2\varphi\,d\psi^2)), \] where \(R =\text{const}\).
He also considers the generalized Bertrand problem and finds all spherical symmetry potentials for which the particle’s orbits are closed. He proves that the generalized Kepler principles are valid.

MSC:
83C10 Equations of motion in general relativity and gravitational theory
70F05 Two-body problems
70H99 Hamiltonian and Lagrangian mechanics
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