Stable Orbits of Rigid, Rotating, Precessing, Massive Rings

Abstract

The dynamics of a rigid, rotating, precessing, massive ring orbiting a point mass within the perimeter of the ring are considered. It is demonstrated that orbits dynamically stable against perturbations in three dimensions exist for a range of rigid body rotation parameters of the ring. Previous analysis and some well-known works of fiction have considered the stability of both rigid and flexible, non-precessing ring systems and found that they are unstable in the plane of the ring unless an active stabilization system is employed. There does not appear to be any analyses previously published considering rigid body precession of such a system or that demonstrate passive stability in three dimensions. Deviations from perfect rigidity and possible applications of such a system are discussed.