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Central configurations of three nested regular polyhedra for the spatial 3n–body problem

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dc.contributor Universitat de Vic. Escola Politècnica Superior
dc.contributor Universitat de Vic. Grup de Recerca en Tecnologies Digitals
dc.contributor.author Corbera Subirana, Montserrat
dc.contributor.author Llibre, Jaume
dc.date.accessioned 2013-04-19T11:55:06Z
dc.date.available 2013-04-19T11:55:06Z
dc.date.created 2009
dc.date.issued 2009
dc.identifier.citation CORBERA SUBIRANA, Montserrat; LLIBRE, Jaume. "Central configurations of three nested regular polyhedra for the spatial 3n-body problem". A: Journal of Geometry and Physics, 2009, vol. 59, núm. 3, pàg. 321-339. ca_ES
dc.identifier.issn 0393-0440
dc.identifier.uri http://hdl.handle.net/10854/2208
dc.description.abstract Three regular polyhedra are called nested if they have the same number of vertices n, the same center and the positions of the vertices of the inner polyhedron ri, the ones of the medium polyhedron Ri and the ones of the outer polyhedron Ri satisfy the relation Ri = ri and Ri = Rri for some scale factors R > > 1 and for all i = 1, . . . , n. We consider 3n masses located at the vertices of three nested regular polyhedra. We assume that the masses of the inner polyhedron are equal to m1, the masses of the medium one are equal to m2, and the masses of the outer one are equal to m3. We prove that if the ratios of the masses m2/m1 and m3/m1 and the scale factors and R satisfy two convenient relations, then this configuration is central for the 3n–body problem. Moreover there is some numerical evidence that, first, fixed two values of the ratios m2/m1 and m3/m1, the 3n–body problem has a unique central configuration of this type; and second that the number of nested regular polyhedra with the same number of vertices forming a central configuration for convenient masses and sizes is arbitrary. ca_ES
dc.format application/pdf
dc.format.extent 36 p. ca_ES
dc.language.iso eng ca_ES
dc.publisher Elsevier ca_ES
dc.rights (c) 2009 Elsevier. Published article is available at: http://dx.doi.org/10.1016/j.geomphys.2008.11.01 ca_ES
dc.subject.other Matemàtica ca_ES
dc.title Central configurations of three nested regular polyhedra for the spatial 3n–body problem ca_ES
dc.type info:eu-repo/semantics/article ca_ES
dc.identifier.doi https://doi.org/10.1016/j.geomphys.2008.11.01
dc.relation.publisherversion http://www.sciencedirect.com/science/article/pii/S0393044008001861
dc.rights.accesRights info:eu-repo/semantics/openAccess ca_ES
dc.type.version info:eu-repo/acceptedVersion ca_ES
dc.indexacio Indexat a SCOPUS
dc.indexacio Indexat a WOS/JCR ca_ES

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