Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1894246 | Journal of Geometry and Physics | 2009 | 16 Pages |
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.