An efficient algorithm for global periodic orbits generation near irregular-shaped asteroids

Periodic orbits (POs) play an important role in understanding dynamical behaviors around natural celestial bodies. In this study, an efficient algorithm was presented to generate the global POs around irregular-shaped uniformly rotating asteroids. The algorithm was performed in three steps, namely global search, local refinement, and model continuation. First, a mascon model with a low number of particles and optimized mass distribution was constructed to remodel the exterior gravitational potential of the asteroid. Using this model, a multi-start differential evolution enhanced with a deflection strategy with strong global exploration and bypassing abilities was adopted. This algorithm can be regarded as a search engine to find multiple globally optimal regions in which potential POs were located. This was followed by applying a differential correction to locally refine global search solutions and generate the accurate POs in the mascon model in which an analytical Jacobian matrix was derived to improve convergence. Finally, the concept of numerical model continuation was introduced and used to convert the POs from the mascon model into a high-fidelity polyhedron model by sequentially correcting the initial states. The efficiency of the proposed algorithm was substantiated by computing the global POs around an elongated shoe-shaped asteroid 433 Eros. Various global POs with different topological structures in the configuration space were successfully located. Specifically, the proposed algorithm was generic and could be conveniently extended to explore periodic motions in other gravitational systems.