Equilibrium Point Evolution and the Associated Characteristic Curves of an Asteroid

Abstract This study investigates the evolution of equilibrium points (EPs) in the dynamical environment of a rotating asteroid, parametrized with respect to a single governing physical parameter. The polyhedral model is employed to accurately represent the asteroid’s gravity field, and the corresponding equations of motion are parametrized using a general variable associated with either the spin rate or bulk density of the asteroid. A theorem is established, demonstrating that the EP sets derived from these two parametrizations are identical under specific conditions, allowing them to be interpreted geometrically as the characteristic curves of an asteroid. To enable a systematic continuation of EP branches, the pseudo-arclength continuation method is utilized. The characteristic curves of asteroids with three representative shape types are presented, along with the demonstration of two corollaries derived from the proposed theorem, which are related to the equal set and subset of the characteristic curves with respect to different general variables. Additionally, a comprehensive stability analysis of EPs along the characteristic curves of two top-shaped asteroids is conducted. Key findings regarding EP classification, the composition of EP branches, and the variation of spin rate are summarized.