The Geometry and Computation of the Dynamics of Coupled Pendula

In this paper, we analyze the dynamics of a system consisting of two torsionally coupled pendula with dissipation and with external forcing. In addition to several general results about the periodic solutions of the system, we prove that a family of homoclinic solutions exists in part of the parameter space, and give computational evidence that part of this family is the type considered by Shil'nikov. The existence of such orbits generates rich dynamics, which we describe qualitatively and illustrate with computed solutions.