Some periodic solutions of a four-body problem. II

Abstract

Further results are obtained for the four-body problem studied in a previous paper. It is shown that the problem can be formulated in two ways as a perturbation of the restricted three-body problem. According to the Lyapunov Center Theorem, there is a family of periodic solutions near a libration point of the restricted three-body problem. Here we prove that corresponding to each periodic solution in an infinite subset of this family, there is a periodic motion of the particle of negligible mass in our four-body problem provided that a single bifurcation equation, which can be formulated explicitly, has a solution.