Computing invariant manifolds for libration point missions

The goal of this lecture is to review several methodologies for the computation of invariant manifolds, having in mind the needs of preliminary mission design of libration point missions. Because of this, the methods reviewed are developed for and applied to the circular, spatial restricted three-body problem (RTBP), although most of them can be applied with few changes, or almost none, to general dynamical systems. The methodology reviewed covers the computation of (families of) fixed points, periodic orbits, and invariant tori, together with the stable and unstable manifolds of all these kinds of invariant objects, and also homoclinic and heteroclinic connections between them. The methods reviewed include purely numerical and semi-analytical ones. No background is assumed except for a graduate level knowledge of calculus, differential equations and basic numerical methods. In particular, the notions from the theory of dynamical systems required for the development of the methods are introduced as needed