The stability of periodic linear oscillations of a satellite about the direction of the major axis of an elliptic orbit

The motion of a satellite about its centre of mass in a central Newtonian gravitational field in an elliptic orbit under arbitrary (both planar and spatial) perturbations is considered. The satellite is a rigid body, whose linear dimensions are small compared with the dimensions of the orbit. The special case of planar periodic motions of the satellite about the direction of the major axis of the orbit of its centre of mass is investigated. The regions of Lyapunov instability and the regions of stability in a first approximation are obtained in the parameter space of the problem.