Coupled Librational Motion of an Axi-Symmetric Satellite in a Circular Orbit

Abstract

The review of the literature suggests that the planar motion of a rigid satellite in a gravity gradient field has been the subject of considerable investigation during the past ten years. In contrast the dynamic study of a satellite executing librational motion out of the orbital plane has received comparatively little attention. Such an investigation is important because as pointed out by Kane, for large amplitudes the transverse motion is strongly coupled with that in the plane.The lack of information may be due to the complex nature of the problem. The non-linear, non-autonomous, coupled equations of motion involving a large number of parameters are not amenable to simple, concise analysis. Some simplification may be achieved by restricting the satellite motion to a circular orbit. For this case, as indicated by Auelmann, closed zero-velocity curves exist under certain conditions which limit the amplitude of motion.