Effect of High-Order Dynamics on Single-Impulse Lissajous-to-Lissajous Transfers around a Collinear Libration Point

Orbital transfers between libration point orbits have played a crucial role in meeting diverse mission constraints around a libration point. Existing analytical theories for such transfers, built on the linearization of the circular restricted three-body problem, have shown promising results in developing transfer strategies. However, given the large excursions of actual mission trajectories, the influence of the neglected high-order dynamics is expected to have a nontrivial effect on these transfers. This study proposes a numerical method that iteratively refines the solutions for impulsive transfers obtained from linear theory, based on the semi-analytical Lindstedt-Poincaré expansion. This method not only provides a means for refinement but also enables systematic validations of linear transfer theories within a broader dynamical framework while retaining orbital parameters. The proposed method is applied to in-plane single-impulse transfers between two Lissajous orbits around a collinear libration point in the Sun-Earth+Moon and Earth-Moon systems. The results show that while the linear solutions remain relatively accurate near optimalities, they are significantly disturbed at the two extremities of the Lissajous orbits by the the high-order dynamics. The deviation from the linear solutions exhibits a clear dependency on parameters such as the in-plane phase, transfer orbit families, and the libration point, leading to either improvements and deteriorations in the overall performance of the transfers. These results provide insights into the validity of existing linear theories and show how the nonlinearity can be leveraged to improve maneuver strategies.