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Title:
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Central configurations of three nested regular polyhedra for the spatial 3n–body problem
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Author:
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Corbera Subirana, Montserrat; Llibre, Jaume
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Other authors:
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Universitat de Vic. Escola Politècnica Superior; Universitat de Vic. Grup de Recerca en Tecnologies Digitals |
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Notes:
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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. |
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Subject(s):
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-Matemàtica |
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Rights:
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(c) 2009 Elsevier. Published article is available at: http://dx.doi.org/10.1016/j.geomphys.2008.11.01
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Document type:
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Article
info:eu-repo/acceptedVersion |
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Published by:
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Elsevier
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