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

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.