Resonance transition periodic orbits in the circular restricted three-body problem

Abstract

This work studies a special type of cislunar periodic orbits in the circular restricted three-body problem called resonance transition periodic orbits, which switch between different resonances and revolve about the secondary with multiple loops during one period. In the practical computation, families of multiple periodic orbits are identified first, and then the invariant manifolds emanating from the unstable multiple periodic orbits are taken to generate resonant homoclinic connections, which are used to determine the initial guesses for computing the desired periodic orbits by means of multiple-shooting scheme. The obtained periodic orbits have potential applications for the missions requiring long-term continuous observation of the secondary and tour missions in a multi-body environment.