Quasi-Periodic Orbit Transfer Design via Whisker Intersection Sets

Abstract

Impulsive maneuver design between quasi-periodic orbits (QPOs) remains a prevalent problem in astrodynamics. Challenges associated with the higher-dimensional nature of QPOs present difficulties when using existing approaches to design transfers between them. This paper establishes a methodology to abate these issues. Fundamental to the approach is the treatment of orbits as tori and their manifolds as the associated whiskers. Utilizing this formulation, intersection curves, surfaces, or volumes between the manifolds are computed leveraging a robust multiparameter continuation scheme. Intersections are then used to seed a multiple shooting scheme to compute transfer trajectories between a pair of orbits. The approach is applied in the Earth–moon circular restricted three-body problem. Numerical examples demonstrate the benefits of considering QPOs in the preliminary stage of trajectory design, showing that leveraging these higher-dimensional solutions offers reductions in propellant cost and transfer time when compared to their periodic counterparts.