Numerical determination of Lissajous trajectories in the restricted three-body problem

Abstract

In previous studies, Lissajous trajectories associated with the collinear libration points in the restricted three-body problem have been successfully computed analytically to at least third-order. Those approximations are utilized to determine such trajectories numerically for an arbitrary, predetermined number of revolutions in the rotating frame, for the case of circular primary motion. The numerical approach first identifies target positions at specified intervals along the trajectory and locates a continuous path through those points with velocity discontinuities. Then the Δv are simultaneously reduced in an iterative process. Such trajectories have been constructed in various primary systems, for a wide range of orbit sizes and a large number of revolutions.