The asymptotic properties of the motions of satellites in a central field due to internal dissipation

A satellite in the form of a system of bodies that does not have the property of a gyrostat in the general case is considered. An algorithm for determining all the equilibrium configurations of the system that correspond to steady motions in a central gravitational field and an algorithm for analysing their stability are given. A method based on Routh's first theorem is used to investigate the asymptotic stability of the steady motions in the unconstrained problem. Three effects caused by internal dissipation are established in a model example: stabilization of the satellites in a neighbourhood of rotations about a normal to the orbital plane, which is codirectional with the axis of the largest moment of inertia, evolution of elliptic orbits into circular orbits, and capture of the satellites in resonant oscillatory modes of motion.