Dynamics of the the dihedral four-body problem

Davide L. Ferrario, Alessandro Portaluri

Research output: Contribution to journalArticlepeer-review

Abstract

Consider four point particles with equal masses in the Euclidean space, subject to the following symmetry constraint: at each instant they are symmetric with respect to the dihedral group D2, that is the group generated by two rotations of angle around two orthogonal axes. Under a homogeneous potential of degree for 0 < < 2, this is a subproblem of the four-body problem, in which all orbits have zero angular momentum and the conguration space is three-dimensional. In this paper we study the ow in McGehee coordinates on the collision manifold, and discuss the qualitative behavior of orbits which reach or come close to a total collision.

Original languageEnglish (US)
Pages (from-to)925-974
Number of pages50
JournalDiscrete and Continuous Dynamical Systems - Series S
Volume6
Issue number4
DOIs
StatePublished - Aug 2013

Keywords

  • Dihedral 4-body problem
  • Heteroclinics
  • McGehee coordinates

ASJC Scopus subject areas

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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