Forced oscillations of singular dynamical systems with an application to the restricted three body problem

Abstract

We consider forced dynamical systems with two degrees of freedom having singular potentials and we prove existence of infinitely many classical (noncollision) periodic solutions. These solutions have a prescribed rotation behavior with respect to the singularities and a prescribed period (the same of the systems). They are obtained variationally as minima of a suitable functional on open subsets of a Hubert space. This investigation was motivated by the elliptic restricted three body problem with arbitrary masses of the two primaries. For that problem we obtain infinitely many distinct “generalized” periodic solutions (i.e., solutions which possibly experience collisions).