Chaotic Trajectories in the Restricted Problem of Three Bodies

Abstract

A complete qualitative understanding of the solutions of a set of nonlinear differential equations requires an investigation of the chaotic properties of the system. The circular restricted problem of three bodies has a long and rich history of qualitative analysis yet few studies have examined the possible existence of chaos in this problem. This study concentrates on the advent of chaos for widely different points in the phase space which correspond to closed Jacobian curves. In addition to observing the non — periodicity of the trajectory, two methods, Liapounov Characteristic Numbers and Poincare Surface of Sections, are used to classify an orbit as chaotic. Regularized and unregularized equations of motion were used in conjunction with a variable — stepsize integrator to produce the orbits.