NONLINEAR DYNAMICS IN AN EXTENDED NEIGHBOURHOOD
OF THE TRANSLUNAR EQUILIBRIUM POINT
Angel Jorba and Josep Masdemont
Dept. de Matematica Aplicada I (ETSEIB), Universitat Politecnica de
Catalunya, Diagonal 647, 08028 Barcelona (Spain).
E-mails: jorba@ma1.upc.es, josep@tere.upc.es
Abstract
We are interested in the motion of a small particle in some regions of
the Earth-Moon system. As a first model, we will use the spatial
Restricted Three Body Problem (RTBP). It is well known that, in
synodic coordinates, this model has five equilibrium points. We will
focus on the one that is behind the Moon, usually called the $L_2$
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 effective 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.
Keywords: Invariant tori, invariant manifolds, central manifolds,
quasiperiodic solutions.