On the nonlinear Poisson bracket arising in nonholonomic mechanics

DOI10.1134/S0001434614030031zbMath1348.70039OpenAlexW2091145302MaRDI QIDQ2341986

Alexey V. Borisov, Ivan. S. Mamaev, Andreĭ Vladimirovich Tsyganov

Publication date: 8 May 2015

Published in: Mathematical Notes (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0001434614030031

zbMATH Keywords

Poisson structuredynamical systemPoisson bracketCasimir functionnonholonomic systemRouth sphereconformally Hamiltonian representationrolling of a Chaplygin ball

Mathematics Subject Classification ID

Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics (70G45) Motion of a rigid body in contact with a solid surface (70E18) Nonholonomic dynamical systems (37J60)

Related Items (1)

Nonintegrability and obstructions to the Hamiltonianization of a nonholonomic Chaplygin top

Cites Work

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• Conservation laws, hierarchy of dynamics and explicit integration of nonholonomic systems
• Rolling of a rigid body on a plane and sphere. Hierarchy of dynamics
• Rolling of a ball on a surface. New integrals and hierarchy of dynamics
• Hamiltonization of non-holonomic systems in the neighborhood of invariant manifolds

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