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Published 1988 | public
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The dynamics of coupled planar rigid bodies. Part I: Reduction, equilibria and stability

Sreenath, N.
Oh, Y. G.
Krishnaprasad, P. S.
Marsden, J. E.
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Abstract

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 ; 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 II. 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.

Additional Information

© Oxford University Press 1988. Received June 1987. The work of the first and third authors was supported in part by the National Science Foundation under grant OIR-85-00108, AFOSR-URI grant AFOSR-87-0073 and by the Minta Martin Fund for Aeronautical Research. The research of the second and fourth authors was partially supported by DOE contract DE-AT03-85ER12097 and by AFOSR-URI grant AFOSR-87-0073.

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August 19, 2023
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