Instabilities in a spinning axi-symmetric rigid satellite

Abstract

It is known that the stability or instability of motion of a rigid axi-symmetric satellite spinning around its axis of symmetry can be determined by knowing its inertia-momentratio and its winding number [1,2]. This classical result is based on a linear stability analysis of the equation of motion which allows very small angular deviations of the satellite's axis of symmetry from the space-fixed Z-direction (see Figure 1.). The present paper sets out to study the full non-linear equations of motion of a spinning satellite without confining its motion to small attitude angles and small perturbations which are necessary in linear stability analysis. To that end, using a normalized Hamiltonian formalism, the nonlinear differential equations of motion of the satellite are obtained. It is shown that the motion of a spinning satellite in a central force field defines a motion on a three dimensional manifold. Various dynamic behaviours e.g. periodic, quasiperiodic, and chaotic are diagnosed via the Poincard map technique. The effect of satellite oblateness on the motion is also studied.