Spatial bi-stacked central configurations formed by two dual regular polyhedra
Corbera Subirana, Montserrat (Universitat de Vic. Departament de Tecnologies Digitals i de la Informació)
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Pérez-Chavela, Ernesto (Universidad Autónoma Metropolitana-Iztapalapa (Mèxic). Departamento de Matemáticas)

Date:	2014
Abstract:	In this paper we prove the existence of two new families of spatial stacked central configurations, one consisting of eight equal masses on the vertices of a cube and six equal masses on the vertices of a regular octahedron, and the other one consisting of twenty masses at the vertices of a regular dodecahedron and twelve masses at the vertices of a regular icosahedron. The masses on the two different polyhedra are in general different. We note that the cube and the octahedron, the dodecahedron and the icosahedron are dual regular polyhedra. The tetrahedron is itself dual. There are also spatial stacked central configurations formed by two tetrahedra, one and its dual.
Grants:	Ministerio de Ciencia e Innovación MTM2008-03437 Agència de Gestió d'Ajuts Universitaris i de Recerca 2009/SGR-410 European Commission 316338 European Commission 318999
Note:	Agraïments: The three authors are partially supported by CONACYT, México, Grant 128790, and by Red de Cuerpos Académicos del PROMEP-México.
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Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	N-body problem ; Spatial central configurations ; Dual regular polyhedra
Published in:	Journal of mathematical analysis and applications, Vol. 413 Núm. 2 (2014) , p. 648-659, ISSN 1096-0813

DOI: 10.1016/j.jmaa.2013.12.015

Postprint 24 p, 448.9 KB

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