An Analytical Approach to In-Plane Asymptotic Three-Impulse Transfers Between Lissajous Orbits Near a Collinear Libration Point

Abstract In this study, we present an analytical framework for in-plane three-impulse transfers between Lissajous orbits near a collinear libration point that have asymptotic invariant manifolds at both ends. The solutions for this type of three-impulse transfer are constructed based on existing results on two-impulse transfers, which approximate bounded single-impulse-like transfers with asymptotic invariant manifolds at one end. The asymptotic property of these invariant manifolds not only reduces the maneuver cost compared to single-impulse and two-impulse transfers but also eliminates the large degree of freedom associated with the problem, enabling a more systematic analysis of the transfer. The proposed analytical framework is applied to the orbital transfer problem between two Lissajous orbits, and the resulting performance and key characteristics and trade-off are investigated. Our numerical analysis shows that this type of transfer achieves approximately an 11% reduction in the maneuver cost across all amplitude ranges, compared to transfers with fewer maneuvers. Additionally, a linear scaling law for the optimal maneuver cost, similar to the one found in existing single-impulse transfer theory, is also identified.