To the problem of plane periodic rotations of a satellite in an elliptic orbit

Abstract

We study the motion of a satellite (a rigid body) with respect to its center of mass in an elliptic orbit of small eccentricity. We analyze the nonlinear problem of the existence and stability of periodic (in the orbital coordinate system) rotations of the satellite with a period multiple of the period of revolution of its center of mass in the orbit. We study the direct and reverse rotations. In particular, we find and investigate the set of bifurcation values of the satellite dimensionless inertial parameter near which the branching of the periodic reverse rotations occurs. We consider three specific examples of application of the obtained general theoretical conclusions. In one of these examples, we prove the stability of the direct resonance rotations of Mercurial type. In the other two examples, we consider the branching problem for reverse rotations with a period whose ratio to the period of motion of the center of mass in the orbit is equal to 1 or 2.