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 language | English (US) |
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Pages (from-to) | 925-974 |
Number of pages | 50 |
Journal | Discrete and Continuous Dynamical Systems - Series S |
Volume | 6 |
Issue number | 4 |
DOIs | |
State | Published - Aug 2013 |
Keywords
- Dihedral 4-body problem
- Heteroclinics
- McGehee coordinates
ASJC Scopus subject areas
- Analysis
- Discrete Mathematics and Combinatorics
- Applied Mathematics