Nonlinear Dynamics in an Extended Neighbourhood of the Translunar Equilibrium Point Angel Jorba and Josep Masdemont

We are interested in the motion of a small particle in some regions of the Earth Moon system As a rst model we will use the spatial Restricted Three Body Problem RTBP see for de nition and main properties It is well known that in synodic coordinates this model has ve equilibrium points We will focus on the one that is behind the Moon usually called the L point Our purpose is to describe the dynamics in an extended neighbourhood of that point This information is very useful to keep an spacecraft there because we can take advantage of the natural dynamics of the problem The main tools used are an e ective computation of the central manifold of the point to give a qualitative description of the dynamics and a Lindstedt Poincar e method to compute invariant tori inside the central manifold This methodology has already been used in similar problems see