Symmetric periodic orbits in the isosceles three body problem

Using global variational methods we establish a family of symmetric periodic orbits of the Isosceles three body problem with arbitrary masses. Stability type may be determined for families of symmetric periodic orbits on the energy-momentum levels by counting Lagrangian singularities (Maslov index) along the orbits. We also present numerical simulations which afford an illustration of the variational-stability method for periodic orbits, as well as providing an overview of the complicated dynamics. The symmetric periodic orbit families admit some surprising regularity (reminiscent of Kepler's third law for scaling of elliptical orbits) amongst a chaotic background.