Equilibria and stability for a gyrostat satellite in circular orbit

Abstract

In this paper, we consider the rotational motion of a gyrostat satellite in a circular Keplerian orbit around a planet. The motion is first considered to be spherical, and in a second case with an axis of symmetry. Firstly, we establish the Newton's equations and we prove that the Hamiltonian system has a non-canonical structure in both cases. In the second part, we consider an approximation of potential of order two to investigate the equilibrium solutions for both problems, and we give sufficient conditions for the non-linear stability whether particularly the gyrostatic momentum is in the principal direction of gyrostat satellite.