Near-Collision Dynamics for Particle Systems with Quasihomogeneous Potentials

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We study collision and ejection orbits of 3-particle systems having the potentialW=U+V, whereUandVare homogeneous functions of degree −aand −b, respectively, with 1⩽a<b. We show that forb≠2, collision and ejection orbits tend to form asymptotically a central configuration. For the caseb=2, which corresponds to Maneff's gravitational law, we find a set of collision and ejection orbits reaching the triple collision manifold without asymptotic phase. This set contains an uncountable union of manifolds and has positive measure within the set of all rectilinear solutions.