On the periodic orbits and the integrability of the regularized Hill lunar problem
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Roberto, Lucy Any (Ibilce - UNESP(Brazil). Departamento de Matemática)

Date:	2011
Abstract:	The classical Hill's problem is a simplified version of the restricted three-body problem where the distance of the two massive bodies (say, primary for the largest one and secondary for the smallest) is made infinity through the use of Hill's variables. The Levi-Civita regularization takes the Hamiltonian of the Hill lunar problem into the form of two uncoupled harmonic oscillators perturbed by the Coriolis force and the Sun action, polynomials of degree 4 and 6, respectively. In this paper we study periodic orbits of the planar Hill problem using the averaging theory. Moreover we provide information about the C1 integrability or non-integrability of the regularized Hill lunar problem.
Grants:	Ministerio de Economía y Competitividad MTM2008-03437 Agència de Gestió d'Ajuts Universitaris i de Recerca 2009/SGR-410
Note:	Agraïments: The second author is partially supported by CAPES/MECD-DGU 015/2010 Brazil and Spain, process number BEX 4251/10-5.
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Periodic orbit ; Averaging method ; Hill lunar problem ; Integrability
Published in:	Journal of Mathematical Physics, Vol. 52 Núm. 8 (2011) , p. 82701, ISSN 1089-7658

DOI: 10.1063/1.3618280

Postprint 9 p, 301.8 KB

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