Bifurcation of relative equilibria of the (1 3)-body problem
Corbera Subirana, Montserrat (Universitat de Vic. Departament de Tecnologies Digitals i de la Informació)
Cors Iglesias, Josep Maria (Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada III)
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Moeckel, Richard (University of Minnesota. School of Mathematics)

Date:	2015
Abstract:	We study the relative equilibria of the limit case of the planar Newtonian 4-body problem when three masses tend to zero, the so-called (1 3)-body problem. Depending on the values of the infinitesimal masses the number of relative equilibria varies from ten to fourteen. Six of these relative equilibria are always convex, and the others are concave. Each convex relative equilibrium of the (1 3)-body problem can be continued to a unique family of relative equilibria of the general 4-body problem when three of the masses are sufficiently small and every convex relative equilibrium for these masses belongs to one of these six families.
Grants:	Ministerio de Economía y Competitividad MTM2008-03437 Ministerio de Economía y Competitividad MTM2013-40998-P Agència de Gestió d'Ajuts Universitaris i de Recerca 2014/SGR-568 European Commission 316338 European Commission 318999
Note:	Agraïments: FEDER-UNAB10-4E-378. R. Moeckel's research is supported by NSF grant DMS-1208908.
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	(1 n)-body problem ; Celestial Mechanics ; Relative equilibria
Published in:	SIAM Journal on Mathematical Analysis, Vol. 47 Núm. 2 (2015) , p. 1377-1404, ISSN 1095-7154

DOI: 10.1137/140978661

Postprint 33 p, 6.0 MB

The record appears in these collections:
Research literature > UAB research groups literature > Research Centres and Groups (research output) > Experimental sciences > GSD (Dynamical systems)
Articles > Research articles
Articles > Published articles