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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.

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