A multi-step method to calculate long-term quasi-periodic orbits around the Sun-Earth L1/L2

Quasi-periodic orbits around the libration point orbits have attracted significant attention since they can provide more opportunities for space missions. This paper proposes a variable step-size multistep method that can effectively calculate long-term quasi-periodic orbits around the Sun-Earth L 1 / L 2 in the Sun-Earth-Moon bicircular model. In this method, periodic orbits in the Sun-Earth L 1 / L 2 serve as the initial reference trajectories for quasi-periodic orbits. Then a two-level multiple shooting is introduced to transition periodic orbits to the short-term quasi-periodic orbits. Finally, a variable step-size multistep method is proposed to obtain long-term quasi-periodic orbits based on the approximately linear relationship between the two-level multiple shooting method and step size. Numerical results show that this method can effectively obtain a large set of long-term quasi-periodic orbits whether the quasi-periodic orbits have free or fixed initial positions. Furthermore, this method is also extended to design long-term quasi-periodic orbits with differential phase angles of the Moon.