Stable Orbits of Rigid, Rotating, Precessing, Massive Rings

TL;DR

This paper demonstrates that a rigid, precessing, massive ring can have dynamically stable orbits around a point mass in three dimensions, a stability not previously shown without active stabilization.

Contribution

It introduces the concept of passive three-dimensional stability for precessing rigid rings, filling a gap in previous analyses of ring stability.

Findings

Stable orbits exist for certain rotation parameters.

Precessing rings can be passively stable in three dimensions.

Previous models lacked analysis of rigid precessing rings' stability.

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.