The Dynamics of Coupled Planar Rigid Bodies.

Abstract

This paper studies the dynamics of coupled planar rigid bodies, concentrating on the case of two bodies coupled with a hinge joint. The Hamiltonian structure is non-canonical and is obtained using the methods of reduction, starting from canonical brackets on the cotangent bundle of the configuration space in material representation. The dynamics on the reduced space occurs on cylinders in R^3; stability of the equilibria is studied using the Energy - Casimir method and is confirmed numerically. The phase space contains a homoclinic orbit which will produce chaotic solutions when the system is perturbed.