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

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 derived explicitly utilizing existing results on two-impulse transfers as a building block, 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 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.