On Orbital Stability of Pendulum-like Satellite Rotations at the Boundaries of Stability Regions

The motion of a rigid body satellite about its center of mass is considered. The problem of the orbital stability of planar pendulum-like rotations of the satellite is investigated. It is assumed that the satellite moves in a circular orbit and its geometry of mass corresponds to a plate. In unperturbed motion the minor axis of the inertia ellipsoid lies in the orbital plane.
A nonlinear analysis of the orbital stability for previously unexplored values of parameters corresponding to the boundaries of the stability regions is carried out. The study is based on the normal form technique. In the special case of fast rotations a normalization procedure is performed analytically. In the general case the coefficients of normal form are calculated numerically. It is shown that in the case under consideration the planar rotations of the satellite are mainly unstable, and only on one of the boundary curves there is a segment where the formal orbital stability takes place.