Article ID Journal Published Year Pages File Type
1894246 Journal of Geometry and Physics 2009 16 Pages PDF
Abstract

In this paper we prove that there are only two different classes of central configurations 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 α=γ=0α=γ=0 and β=πβ=π 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 α=γ=0α=γ=0 and β=πβ=π of the other two.In all of these cases we have assumed that the masses on each tetrahedron are equal but masses on different tetrahedra could be different.

Related Topics
Physical Sciences and Engineering Mathematics Mathematical Physics
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