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 = 0 and β = 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 = 0 and β = 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. © 2009 Elsevier B.V. All rights reserved.
Original language | English |
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Pages (from-to) | 1379-1394 |
Journal | Journal of Geometry and Physics |
Volume | 59 |
DOIs | |
Publication status | Published - 1 Oct 2009 |
Keywords
- Classical mechanics
- Nested regular tetrahedra
- Spatial central configurations
- n-body problem