High-order expansions of invariant manifolds of libration point orbits with applications to mission design

Abstract

This paper deals with two methodologies for computing the stable and unstable manifolds of libration point orbits in series expansions. One of the procedures is based on the Lindstedt–Poincaré method, the other one on a normal form of the Hamiltonian equations of motion, and, from a geometrical point of view, both methodologies complement each other. The tools resulting from the analysis are applied in the framework of the restricted three-body problem and in the Hill problem. As examples of applicability, we consider situations dealing with usual needs related to mission analysis of libration point orbits, as well as the computation of asymptotic orbits between invariant tori.