The dynamics of coupled planar rigid bodies. II: Bifurcations, periodic solutions, and chaos

DOI10.1007/BF01053929zbMath0693.70021MaRDI QIDQ908729

P. S. Krishnaprasad, Yong-Geun Oh, Jerrold E. Marsden, Narasingarao Sreenath

Publication date: 1989

Published in: Journal of Dynamics and Differential Equations (Search for Journal in Brave)

zbMATH Keywords

stability analysisstable equilibriumMelnikov's methodequivariant Weinstein-Moser theoremexistence of two periodic orbitsPoincaré-Birkhoff-Smale horseshoesrelative equilibria of the dynamics of three coupled planar rigid bodies

Mathematics Subject Classification ID

Stability for nonlinear problems in mechanics (70K20) Hamilton's equations (70H05) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99) Dynamics of a rigid body and of multibody systems (70E99)

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Cites Work

• Hamiltonian structures and stability for rigid bodies with flexible attachments
• Generic bifurcation of Hamiltonian systems with symmetry. With an appendix by Jerrold Marsden
• A stability criterion for Hamiltonian systems with symmetry
• The Hamiltonian structure of nonlinear elasticity: The material and convective representations of solids, rods, and plates
• Normal modes for nonlinear Hamiltonian systems
• Stable and Random Motions in Dynamical Systems
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• The dynamics of coupled planar rigid bodies. Part I: reduction, equilibria and stability
• Periodic orbits near an equilibrium and a theorem by Alan Weinstein
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