NEAR-COLLISION DYNAMICS FOR PARTICLE-SYSTEMS WITH QUASI-HOMOGENEOUS POTENTIALS

We study collision and ejection orbits of 3-particle systems having th e potential W = U + V where CI and V are homogeneous functions of degr ee -a and -b, respectively, with 1 less than or equal to a < b. We sho w that for b not equal 2, collision and ejection orbits tend to form a symptotically a central configuration. For the case b = 2, which corre sponds to Maneff's gravitational law, we find a set of collision and e jection orbits reaching the triple collision manifold without asymptot ic phase. This set contains an uncountable union of manifolds and has positive measure within the set of all rectilinear solutions. (C) 1996 Academic Press, Inc.