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Dynamics of the the dihedral four-body problem

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  • Consider four point particles with equal masses in the euclideanspace,subject to the following symmetry constraint: at each instant theyare symmetric with respect to the dihedral group $D_2$,that is the groupgenerated by two rotations of angle $\pi$ around twoorthogonal axes.Under ahomogeneous potential of degree $-\alpha$ for $0<\alpha<2$,this is a subproblem of the four-body problem,inwhich all orbits have zero angular momentum and the configurationspace is three-dimensional.In this paper westudy the flow in McGehee coordinates on the collision manifold,anddiscuss the qualitative behavior of orbits which reach or come close to a total collision.
    Mathematics Subject Classification: Primary: 70F15; Secondary: 70F10, 70F16.

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