On the central configurations in the spatial 5-body problem with four equal masses
Álvarez-Ramírez, Martha (Universidad Autónoma Metropolitana-Iztapalapa (Mèxic). Departamento de Matemáticas)
Corbera Subirana, Montserrat (Universitat de Vic - Universitat Central de Catalunya. Departament de Tecnologies Digitals i de la Informació)
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Date:	2016
Abstract:	We analyze the families of central configurations of the spatial 5-body problem with four masses equal to 1 when the fifth mass m varies from 0 to (Formula presented. ). In particular we continue numerically, taking m as a parameter, the central configurations (which all are symmetric) of the restricted spatial ((Formula presented. ))-body problem with four equal masses and (Formula presented. ) to the spatial 5-body problem with equal masses (i. e. (Formula presented. )), and viceversa we continue the symmetric central configurations of the spatial 5-body problem with five equal masses to the restricted ((Formula presented. ))-body problem with four equal masses. Additionally we continue numerically the symmetric central configurations of the spatial 5-body problem with four equal masses starting with (Formula presented. ) and ending in (Formula presented. ), improving the results of Alvarez-Ramírez et al. (Discrete Contin Dyn Syst Ser S 1: 505-518, 2008). We find four bifurcation values of m where the number of central configuration changes. We note that the central configurations of all continued families varying m from 0 to (Formula presented. ) are symmetric.
Grants:	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 Ministerio de Economía y Competitividad UNAB10-4E-378
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Spatial central configurations ; 5-Body problem ; Bifurcations
Published in:	Celestial Mechanics and Dynamical Astronomy, Vol. 124, Issue 4 (April 2016) , p. 433-456, ISSN 1572-9478

DOI: 10.1007/s10569-015-9670-z

Postprint 26 p, 545.3 KB

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