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This paper studies the dynamics of coupled planar rigid bodies, concentrating on the case of two or three 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 for two bodies occurs on cylinders in R3; stability of the equilibria is studied using the energy-Casimir method and is confirmed numerically. The phase space of the two bodies contains a homoclinic orbit which produces chaotic solutions when the system is perturbed by a third body. This and a study of periodic orbits are discussed in part 11. The number and stability of equilibria and their bifurcations for three bodies as system parameters are varied are studied here; in particular, it is found that there are always four or six equilibria.

Modeling, controllability and control synthesis of two coupled rigid body system with motions in three dimensional space is considered. Angular momentum preserving reorientation problem of interest here has applications in multibody satellites and space robotics, and, in the understanding of the classical cat fall problem. A coordinate free representation of the system dynamics is derived. Assuming a zero angular momentum condition results in a nonholonomic constraint. Controllability and synthesis issues are studied.

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