Dynamics of a point in the axisymmetric gravitational potential of a massive fixed ring and center

A. V. Sakharov

Moscow Institute of Physics and Technology (National Research University), Dolgoprudny, Moscow Oblast, Russia

Abstract: We consider the problem of three-dimensional motion of a passively gravitating point in the potential created by a homogeneous thin fixed ring and a massive point located in the center of the ring. The motion of a passively gravitating point admits two first integrals. We first consider the integrable case of an invariant motion in the equatorial plane and then consider the general case of three-dimensional motion, where we classify the possible trajectories of a point depending on the values of the first integrals. Finally, some previous results for similar problems are compared.

Keywords: celestial mechanics, axisymmetric potential, gravitational potential, ring, phase portrait, first integral, bifurcation.

PACS: 45.50.Pk

MSC: 70F15, 85A05

Received: 04.12.2020
Revised: 31.12.2020

DOI: 10.4213/tmf10020

 English version: Theoretical and Mathematical Physics, 2021, 207:2, 678–688

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