Geodesic
Some Trajectories of a Point in the Potential of a Fixed Ring and Center
Russian journal of nonlinear dynamics, Tome 15 (2019) no. 4, pp. 587-592

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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 space, first integrals
Mots-clés : phase portrait, bifurcations. 
@article{ND_2019_15_4_a18,
     author = {A. V. Sakharov},
     title = {Some {Trajectories} of a {Point} in the {Potential} of a {Fixed} {Ring} and {Center}},
     journal = {Russian journal of nonlinear dynamics},
     pages = {587--592},
     publisher = {mathdoc},
     volume = {15},
     number = {4},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ND_2019_15_4_a18/}
}
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A. V. Sakharov. Some Trajectories of a Point in the Potential of a Fixed Ring and Center. Russian journal of nonlinear dynamics, Tome 15 (2019) no. 4, pp. 587-592. http://geodesic.mathdoc.fr/item/ND_2019_15_4_a18/