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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Rectangular orbits of the curved 4-body problem
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by Florin Diacu and Brendan Thorn PDF
Proc. Amer. Math. Soc. 143 (2015), 1583-1593 Request permission

Abstract:

We consider the $4$-body problem in spaces of constant curvature and study the existence of spherical and hyperbolic rectangular solutions, i.e. equiangular quadrilateral motions on spheres and hyperbolic spheres. We focus on relative equilibria (orbits that maintain constant mutual distances) and rotopulsators (configurations that rotate and change size, but preserve equiangularity). We prove that when such orbits exist, they are necessarily spherical or hyperbolic squares, i.e. equiangular equilateral quadrilaterals.
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Additional Information
  • Florin Diacu
  • Affiliation: Pacific Institute for the Mathematical Sciences, and Department of Mathematics and Statistics, University of Victoria, P.O. Box 1700 STN CSC, Victoria, BC, Canada V8W 2Y2
  • Email: diacu@uvic.ca
  • Brendan Thorn
  • Affiliation: Department of Mathematics and Statistics, University of Victoria, P.O. Box 1700 STN CSC, Victoria, BC, Canada V8W 2Y2
  • Email: bthorn@uvic.ca
  • Received by editor(s): February 21, 2013
  • Received by editor(s) in revised form: July 30, 2013
  • Published electronically: November 4, 2014
  • Communicated by: Walter Craig
  • © Copyright 2014 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 143 (2015), 1583-1593
  • MSC (2010): Primary 34C25, 37J45, 70F10
  • DOI: https://doi.org/10.1090/S0002-9939-2014-12326-4
  • MathSciNet review: 3314071