An Analytical Framework for In-Plane Two-Impulse Transfers Between Lissajous Orbits

Abstract This paper presents an analytical framework for in-plane two-impulse transfers between two Lissajous orbits around a single collinear libration point in the linearized circular restricted three-body problem. Based on the categorization of orbits near a collinear libration point in the linearized dynamics, we formulate two-impulse transfers as a two-point boundary value problem with a fixed time of flight (ToF). We explicitly derive and numerically verify the solution, along with its subsets corresponding to transfers involving asymptotic invariant manifolds. Additionally, we derive some general properties of solutions, including the inherent constraints arising from the limited distribution of invariant manifolds are identified and compared to their single-impulse counterparts. We further investigate the relation between the performance and the constraints of two-impulse transfers by numerically evaluating the cost of maneuvers for amplitude-decreasing transfers. Our main results demonstrate improved feasibility compared to the single-impulse transfers with minimum additional cost for a relatively large ToF, regardless of the size of the amplitude size, as well as the existence of a lower bound on the cost similar to the one found in the single-impulse case.