Central configurations of nested rotated regular tetrahedra

M. Corbera, J. Llibre

Research output: Contribution to journalArticleResearchpeer-review

2 Citations (Scopus)

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 languageEnglish
Pages (from-to)1379-1394
JournalJournal of Geometry and Physics
Volume59
DOIs
Publication statusPublished - 1 Oct 2009

Keywords

  • Classical mechanics
  • Nested regular tetrahedra
  • Spatial central configurations
  • n-body problem

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