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

    2019, Vol. 15, no. 4, pp.  587-592

    Author(s): Sakharov  A. V.

    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
    Citation: Sakharov A. V., Some Trajectories of a Point in the Potential of a Fixed Ring and Center, Rus. J. Nonlin. Dyn., 2019, Vol. 15, no. 4, pp.  587-592

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    [1] Binney, J. and Tremaine S., Galactic Dynamics, 3rd ed., Princeton Univ. Press, Princeton, N.J., 1994, xv, 733 pp.  mathscinet
    [2] Kutuzov, S. A., “Orbits in “Disk + Halo” Galaxy Model”, Order and Chaos in Stellar and Planetary Systems, ASP Conf. Proc., 316, eds. G. G. Byrd et al., Astronomical Society of the Pacific, San Francisco, 2004, 37–42  adsnasa
    [3] Duboshin, G. N., The Theory of Attraction, Fizmatlit, Moscow, 1961, 288 pp. (Russian)
    [4] Lass, H. and Blitzer, L., “The Gravitational Potential due to Uniform Disks and Rings”, Celestial Mech., 30:3 (1983), 225–228  crossref  mathscinet  zmath  adsnasa
    [5] Broucke, R. A. and Elipe, A., “The Dynamics of Orbits in a Potential Field of a Solid Circular Ring”, Regul. Chaotic Dyn., 10:2 (2005), 129–143  mathnet  crossref  mathscinet  zmath  adsnasa
    [6] Tresaco, E., Elipe, A., and Riaguas, A., “Dynamics of a Particle under the Gravitational Potential of a Massive Annulus: Properties and Equilibrium Description”, Celestial Mech. Dynam. Astronom., 111:4 (2011), 431–447  crossref  mathscinet  zmath  adsnasa  elib
    [7] Alberti, A. and Vidal, C., “Dynamics of a Particle in a Gravitational Field of a Homogeneous Annulus Disk”, Celestial Mech. Dynam. Astronom., 98:2 (2007), 75–93  crossref  mathscinet  zmath  adsnasa
    [8] Sidorenko, V. V., “Dynamics of “Jumping” Trojans: A Perturbative Treatment”, Celestial Mech. Dynam. Astronom., 130:10 (2018), 67, 18 pp.  crossref  mathscinet  adsnasa

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