A Multivalued Approach to the Planar Isosceles Three Body Problem

Abstract

The isosceles three body problem consists of three point masses located on the vertices of an isosceles triangle on the plane. The two masses on the asymmetric edge are equal. This problem has been extensively studied but not as a perturbation of the Kepler problem. In this case we arrive at a differential inclusion as a natural formulation when we regularize the problem. We also derive an extension of the vectorfield that allows us to consider orbits across singular sets.