Nonlinear dynamics of displaced non-Keplerian orbits with low-thrust propulsion

Abstract

This paper discusses the stability, transition and control of displaced non-Keplerian orbits by the spacecraft using low-thrust propulsion. The two-body dynamical model developed in the polar coordinates is parameterized by the thrust pitch angle, and then two of the hyperbolic and elliptic equilibria are solved from it. The bounded motions near two equilibria are investigated by dynamical system techniques to find out all the stable and unstable periodic trajectories, and two scenarios of the resonant periodic trajectory are presented. Regardless of the thrust pitch angle, all the transit orbits are numerically demonstrated to be restricted inside the invariant manifolds of Lyapunov orbit near the hyperbolic equilibrium. Then the transit orbits can be distinguished from non-transit ones by the restriction of three-dimensional invariant manifolds projected onto the Poincaré section or position space. Based on the influence of thrust direction on the system topology, operating the thrust pitch angle is an effective tool to achieve the transfer within different types of KAM tori, or even transfer beyond the KAM tori.