Dynamic Characteristics of Periodic Motions in a Restricted N-Body Problem

Abstract

We investigate the existence and follow the evolution and dynamic stability of periodic motions in a restricted version of the N-body problem, where the positions of the mass bodies reside persistently on a planar polygon ring and its geometrical centre. The results show the existence of both (linearly) stable and unstable periodic orbits around the body placed on the ring centre (inside the ring), around all the periphery bodies (outside the ring) and around one or more of the periphery bodies. The stable periodic trajectories form regions of gravitational stability, whereas some classes of the unstable orbits exhibit bifurcations to non-symmetric periodic orbits of the same period, and less often period-doubling bifurcations.