Orbital Transfer Problem on the Central Manifold of Libration Points

The Circular Restricted Three-body Problem (CR3BP) exhibits highly complex nonlinear dynamical characteristics in the vicinity of its libration points. The various periodic and quasi-periodic orbits within this region hold significant value for increasingly complex deep space exploration missions, offering more possibilities and flexibility in the design and control of mission trajectories. The issue of orbit transfers between these libration points warrants systematic investigation. To compute orbits around libration points, a numerical computation method based on escape time is proposed, enabling the unified calculation of various quasi-periodic orbits across a broad range of energy levels. Based on the manifold configuration of libration point orbit state points, a universal orbit maintenance strategy called state-adjoint techniques is proposed, yielding schemes that can sustain long-term stable operation of various libration point orbits. Building on extensive studies of invariant manifolds and Poincaré sections associated with numerous libration point orbits, a comprehensive solution has been designed to enable orbit transfers between libration points through pulse maneuvers. This method fully leverages the dynamical features of libration points and has been proven effective through simulation validation, offering new insights for research on libration point orbit transfers.