Аннотация:
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.
Ключевые слова:
celestial mechanics, axisymmetric potential, center, ring, phase portrait, phase space, first integrals, bifurcations.
Поступила в редакцию: 30.05.2019 Принята в печать: 01.10.2019
Образец цитирования:
A. V. Sakharov, “Some Trajectories of a Point in the Potential of a Fixed Ring and Center”, Rus. J. Nonlin. Dyn., 15:4 (2019), 587–592
\RBibitem{Sak19}
\by A. V. Sakharov
\paper Some Trajectories of a Point in the Potential of a Fixed Ring and Center
\jour Rus. J. Nonlin. Dyn.
\yr 2019
\vol 15
\issue 4
\pages 587--592
\mathnet{http://mi.mathnet.ru/nd686}
\crossref{https://doi.org/10.20537/nd190418}
\elib{https://elibrary.ru/item.asp?id=43248258}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85079522173}
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/nd686
https://www.mathnet.ru/rus/nd/v15/i4/p587
Эта публикация цитируется в следующих 1 статьяx:
А. В. Сахаров, “Динамика точки в осесимметричном гравитационном потенциале кольца и центра”, ТМФ, 207:2 (2021), 319–330; A. V. Sakharov, “Dynamics of a point in the axisymmetric gravitational potential of a massive fixed ring and center”, Theoret. and Math. Phys., 207:2 (2021), 678–688
Цитирование в формате AMSBIB
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