On the Orbital Stability of Pendulum Oscillations of a Dynamically Symmetric Satellite

Abstract

The orbital stability of planar pendulum-like oscillations of a satellite about its center of mass is investigated. The satellite is supposed to be a dynamically symmetrical rigid body whose center of mass moves in a circular orbit. Using the recently developed approach [1], local variables are introduced and equations of perturbed motion are obtained in a Hamiltonian form. On the basis of the method of normal forms and KAM theory, a nonlinear analysis is performed and rigorous conclusions on orbital stability are obtained for almost all parameter values. In particular, the so-called case of degeneracy, when it is necessary to take into account terms of order six in the expansion of the Hamiltonian function, is studied.