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 Nelin. Dinam., 2019, Volume 15, Number 4, Pages 505–512 (Mi nd677)

Nonlinear Stability Analysis of Relative Equilibria of a Solid Carrying a Movable Point Mass in the Central Gravitational Field

O. V. Kholostova

Moscow Aviation Institute (National Research University), Volokolamskoe sh. 4, GSP-3, A-80, Moscow, 125993 Russia

Abstract: The motion of a solid (satellite) carrying a moving point mass in the central Newtonian gravitational field in an elliptical orbit of arbitrary eccentricity is considered. The law of motion of a point mass is assumed to allow for the existence of relative equilibria of the “body-point” system in the orbital coordinate system. A nonlinear stability analysis of these equilibria is carried out, based on the construction and normalization of the area-preserving mapping generated by the motions of the system.

Keywords: solid carrying a point mass, elliptical orbit, relative equilibrium, stability, resonance

 Funding Agency Grant Number Russian Foundation for Basic Research 17-01-00123 This research was supported by the Russian Foundation for Basic Research (project No. 17-01-00123).

DOI: https://doi.org/10.20537/nd190409

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MSC: 70H14, 70H15, 70M20
Accepted:01.08.2019

Citation: O. V. Kholostova, “Nonlinear Stability Analysis of Relative Equilibria of a Solid Carrying a Movable Point Mass in the Central Gravitational Field”, Nelin. Dinam., 15:4 (2019), 505–512

Citation in format AMSBIB
\Bibitem{Kho19} \by O. V. Kholostova \paper Nonlinear Stability Analysis of Relative Equilibria of a Solid Carrying a Movable Point Mass in the Central Gravitational Field \jour Nelin. Dinam. \yr 2019 \vol 15 \issue 4 \pages 505--512 \mathnet{http://mi.mathnet.ru/nd677} \crossref{https://doi.org/10.20537/nd190409}