Geodesic
Dynamics of a point in the axisymmetric gravitational potential of a massive fixed ring and center
Teoretičeskaâ i matematičeskaâ fizika, Tome 207 (2021) no. 2, pp. 319-330 Cet article a éte moissonné depuis la source Math-Net.Ru

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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, first integral
Mots-clés : phase portrait, bifurcation. 
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A. V. Sakharov. Dynamics of a point in the axisymmetric gravitational potential of a massive fixed ring and center. Teoretičeskaâ i matematičeskaâ fizika, Tome 207 (2021) no. 2, pp. 319-330. http://geodesic.mathdoc.fr/item/TMF_2021_207_2_a10/

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