On the bi-Hamiltonian structure of the Chaplygin and Borisov-Mamaev-Fedorov systems at a zero constant of areas. II

MaRDI QIDQ6654703

A. V. Tsiganov

Publication date: 20 December 2024

Published in: Nelineĭnaya Dinamika (Search for Journal in Brave)

zbMATH Keywords

Poisson bracketsnonholonomic mechanicsChaplygin sphere

Mathematics Subject Classification ID

Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Poisson manifolds; Poisson groupoids and algebroids (53D17) Constrained dynamics, Dirac's theory of constraints (70H45) Nonholonomic systems related to the dynamics of a system of particles (70F25) Motion of a rigid body in contact with a solid surface (70E18) Nonholonomic dynamical systems (37J60)

Cites Work

• Integrable Euler top and nonholonomic Chaplygin ball
• Conservation laws, hierarchy of dynamics and explicit integration of nonholonomic systems
• Chaplygin ball over a fixed sphere: an explicit integration
• Explicit integration of one problem in nonholonomic mechanics
• Integrable one-particle potentials related to the Neumann system and the Jacobi problem of geodesic motion on an ellipsoid.
• Ueber Bewegungen eines Punktes.
• Generalizations of classical integrable nonholonomic rigid body systems
• The Stäckel systems and algebraic curves
• INTEGRABLE CASES OF THE DYNAMICS OF A RIGID BODY, AND INTEGRABLE SYSTEMS ON THE SPHERESSⁿ
• Linear r-matrix algebra for classical separable systems
• Duality between integrable Stäckel systems
• Generalized Chaplygins transformation and explicit integration of a system with a spherical support

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