THE SCHWARZSCHILD-TYPE TWO-BODY PROBLEM: A TOPOLOGICAL VIEW

Abstract

The Schwaxzschild-type two-body problem (associated to a force function of the form A/r+B/r³, A,B>0), which models several problems of nonlinear particle dynamics, is being tackled from the standpoint of topology. The corresponding mechanical system is fully characterized, and the first integrals of energy and angular momentum are pointed out. These integrals are used to settle the invariant manifolds and the bifurcation set for the whole allowed interplay among the field parameters, the total energy level, and the angular momentum. The orbits on each manifold are interpreted in terms of physical motion. Besides recovering motions characteristic to classical models, entirely new types of motion are found.