Order and Chaos in the Two-Body Problem

We investigate a simple extension of the classical two-body problem involving the gravitational interaction of a point and a line segment. We find families of periodic orbits amidst chaotic orbits in both the parameter and initial condition spaces. We characterize the dynamics using animations, Poincare sections, distance metrics, power spectral densities, and Lyapunov exponents. This work was supported in part by NSF DMR-0649112.