Invariant manifolds around artificial equilibrium points for low-thrust propulsion spacecraft

Abstract

Low-thrust propulsion is incorporated into circular restricted three-body problem to balance the gravitational and centrifugal forces, and then artificial equilibrium points can be generated. The linear dynamics indicates that there are stable and unstable artificial equilibrium points. Around the unstable artificial equilibrium points, there are center and hyperbolic invariant manifolds. In this work, invariant manifolds around artificial equilibrium points are expressed as formal series of amplitudes corresponding to hyperbolic and center dynamics, and high-order series solutions are constructed up to an arbitrary order. By taking advantage of the series expansions constructed, the motions around unstable artificial equilibrium points can be parameterized. In order to check the validity, the practical convergence of series solutions truncated at different orders is considered. Finally, series expansions of invariant manifolds are applied to designing transfer trajectories from the primary to periodic orbits around artificial equilibrium points which are located inside $L_{1}$ and beyond $L_{2}$ points.