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 Nelin. Dinam., 2019, Volume 15, Number 4, Pages 587–592 (Mi nd686)

Some Trajectories of a Point in the Potential of a Fixed Ring and Center

A. V. Sakharov

Moscow Institute of Physics and Technology, Inststitutskii per. 9, Dolgoprudny, 141700 Russia

Abstract: The problem of three-dimensional motion of a passively gravitating point in the potential created by a homogeneous thin fixed ring and a point located in the center of the ring is considered. Motion of the point allows two first integrals. In the paper equilibrium points and invariant manifolds of the phase space of the system are found. Motions in them are analyzed. Bifurcations in the phase plane corresponding to the motion in the equatorial plane are shown.

Keywords: celestial mechanics, axisymmetric potential, center, ring, phase portrait, phase space, first integrals, bifurcations

DOI: https://doi.org/10.20537/nd190418

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MSC: 70F15, 70G10, 70H03, 70H06, 70H07, 70H33
Accepted:01.10.2019

Citation: A. V. Sakharov, “Some Trajectories of a Point in the Potential of a Fixed Ring and Center”, Nelin. Dinam., 15:4 (2019), 587–592

Citation in format AMSBIB
\Bibitem{Sak19} \by A. V. Sakharov \paper Some Trajectories of a Point in the Potential of a Fixed Ring and Center \jour Nelin. Dinam. \yr 2019 \vol 15 \issue 4 \pages 587--592 \mathnet{http://mi.mathnet.ru/nd686} \crossref{https://doi.org/10.20537/nd190418}