Numerical Determination of Lissajous Trajectories in the Restricted Three-Body Problem
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 ?v 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.
K. C. Howell and H. Pernicka, "Numerical Determination of Lissajous Trajectories in the Restricted Three-Body Problem," Celestial Mechanics, Kluwer Academic Publishers, Jan 1987.
The definitive version is available at https://doi.org/10.1007/BF01238756
Mechanical and Aerospace Engineering
Article - Journal
© 1987 Kluwer Academic Publishers, All rights reserved.