On the stability of tetrahedral relative equilibria in the positively curved 4-body problem

Florin Diacu, Regina Martínez, Ernesto Pérez-Chavela, Carles Simó

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20 Citations (Scopus)

Abstract

We consider the motion of point masses givenby anatural extension of Newtonian gravitationto spaces of constant positive curvature, in which the gravitational attraction between the bodies acts along geodesics. We aim to explore the spectral stability of tetrahedral orbits of the corresponding 4-body problem in the 2-dimensional case, a situation that can be reduced to studying the motion of the bodies on the unit sphere. We first perform some extensive and highly precise numerical experiments to find the likely regions of stability and instability, relative to the values of the masses and to the latitude of the position of the three equal masses. Then we support the numerical evidence with rigorous analytic proofs in the vicinity of some limit cases in which certain masses are either very large or negligible, or the latitude is close to zero. © 2013 Elsevier B.V. All rights reserved.
Original languageEnglish
Pages (from-to)21-35
JournalPhysica D: Nonlinear Phenomena
Volume256-257
DOIs
Publication statusPublished - 1 Aug 2013

Keywords

  • 4-body problem
  • Spaces of constant curvature
  • Stability
  • Tetrahedral orbits

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