TITLE:
Numerical Study of the Geometry of the Phase Space of the Augmented
Hill Three-Body Problem

AUTHORS:
Ariadna Farres^(1), Angel Jorba^(2) and Josep-Maria Mondelo^(3)

(1) Institut de Matematica, Universitat de Barcelona
(2) Departament de Matematiques i Informatica, Universitat de Barcelona
(3) Departament de Matematiques, Universitat Autonoma de Barcelona

E-mails: ariadna.farres@maia.ub.es, angel@maia.ub.es, jmm@mat.uab.cat

ABSTRACT:
The Augmented Hill Three-Body problem is an extension of the classical
Hill problem that, among other applications, has been used to model
the motion of a solar sail around an asteroid. This model is a 3
degrees of freedom (3DoF) Hamiltonian system that depends on four
parameters. This paper describes the bounded motions (periodic orbits
and invariant tori) in an extended neighbourhood of some of the
equilibrium points of the model. An interesting feature is the
existence of equilibrium points with a 1:1 resonance, whose
neighbourhood we also describe. The main tools used are the
computation of periodic orbits (including their stability and
bifurcations), the reduction of the Hamiltonian to centre manifolds at
equilibria, and the numerical approximation of invariant tori. It is
remarkable how the combination of these techniques allows the
description of the dynamics of a 3DoF Hamiltonian system.