Numerical study of the geometry of the phase space of the augmented Hill three-body problem
Farrés, Ariadna (Universitat de Barcelona. Institut de Matemàtiques)
Jorba, Àngel (Universitat de Barcelona. Departament de Matemàtiques i Informàtica)
Mondelo González, José María (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Date:	2017
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.
Grants:	Ministerio de Economía y Competitividad MTM2015-67724-P Ministerio de Economía y Competitividad MTM2013-41168-P Ministerio de Economía y Competitividad MTM2016-80117-P Ministerio de Economía y Competitividad MTM2014-52209-C2-1-P Agència de Gestió d'Ajuts Universitaris i de Recerca 2014/SGR-1145
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Hill 3-Body problem ; Periodic orbits ; Invariant tori ; Centre manifolds ; 1:1 resonance
Published in:	Celestial Mechanics and Dynamical Astronomy, 2017 , ISSN 1572-9478

DOI: 10.1007/s10569-017-9762-z

Postprint 31 p, 6.8 MB

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