On the stability of planar oscillations of a satellite-plate in the case of essential type resonance

We consider satellite motion about its center of mass in a circle orbit. We study the problem of orbital stability for planar pendulum-like oscillations of the satellite. It is supposed that the satellite is a rigid body whose mass geometry is that of a plate. We assume that on the unperturbed motion the middle or minor inertia axis of the satellite lies in the orbit plane, i.e., the plane of the satellite-plate is perpendicular to the plane of the orbit. In this paper we perform a nonlinear analysis of the orbital stability of planar pendulum-like oscillations of a satellite-plate for previously unexplored parameter values corresponding to the boundaries of regions of stability in the first approximation, where the essential type resonances take place. It is proved that on the mentioned boundaries the planar pendulum-like oscillations are formally orbital stable or orbitally stable in third approximation.