HARRINGTONS HAMILTONIAN IN THE STELLAR PROBLEM OF 3 BODIES - REDUCTIONS, RELATIVE EQUILIBRIA AND BIFURCATIONS

We study Harrington's Hamiltonian in the Hill approximation of the stellar problem of three bodies in order to clarify and sharpen a qualitative analysis made by Lidov and Ziglin. We show how the orbital space after four reductions is a two-dimensional sphere, Harrington's Hamiltonian defining a biparametric dynamical system. We produce the diagrams corresponding to each type of phase flow according to a complete discussion of all possible local and global bifurcations determined by the four integrals of the system.