2011/12/20 by Davide L. Ferrario, Ferrario, Davide L., Алессандро Порталури +2
Engineering · Mathematics · Physics and Astronomy · #70F10 (Primary) 37C80 (Secondary) #Astro and Planetary Science #Dynamical Systems (math.DS) #FOS: Mathematics #Quantum chaos and dynamical systems #Spacecraft Dynamics and Control #math.DS #msc:37C80 #msc:70F10
paper · pdf · doi:10.48550/arxiv.1112.4623
46 pages, 5 figures
arxiv created 2011/12/20 · openalex publication_date 2011/12/20 · arxiv updated 2011/12/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 π around two orthogonal axes. Under a homogeneous potential of degree -α for 0<α<2, this is a subproblem of the four-body problem, in which all orbits have zero angular momentum and the configuration space is three-dimensional. In this paper we study the flow in McGehee coordinates on the collision manifold, and discuss the qualitative behavior of orbits which reach or come close to a total collision.