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Central configurations of nested rotated regular tetrahedra

Central configurations of nested rotated regular tetrahedra
 
Corbera Subirana, Montserrat ; Llibre, Jaume
2009

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Enllaç permanent: http://hdl.handle.net/10854/2206
 
Versió de l'editor: https://doi.org/10.1016/j.geomphys.2009.07.004
 

Abstract

In this paper we prove that there are only two different classes of central configura- tions with convenient masses located at the vertices of two nested regular tetrahedra: either when one of the tetrahedra is a homothecy of the other one, or when one of the tetrahedra is a homothecy followed by a rotation of Euler angles = ...»»»»
In this paper we prove that there are only two different classes of central configura- tions with convenient masses located at the vertices of two nested regular tetrahedra: either when one of the tetrahedra is a homothecy of the other one, or when one of the tetrahedra is a homothecy followed by a rotation of Euler angles = = 0 and = of the other one. We also analyze the central configurations with convenient masses located at the vertices of three nested regular tetrahedra when one them is a homothecy of the other one, and the third one is a homothecy followed by a rotation of Euler angles = = 0 and = of the other two. In all these cases we have assumed that the masses on each tetrahedron are equal but masses on different tetrahedra could be different.^^^^

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(c) 2007 Elsevier. Published article is available at: http://dx.doi.org/10.1016/j.geomphys.2009.07.004

Citation:

CORBERA SUBIRANA, Montserrat; LLIBRE, J. "Central configurations of nested rotated regular tetrahedra". A: Journal of Geometry and Physics, 2009, vol. 59, núm. 10, pàg. 1379-1394.