One family of conformally Hamiltonian systems

DOI10.1007/s11232-012-0128-0zbMath1282.81104OpenAlexW2082622295MaRDI QIDQ393958

Andreĭ Vladimirovich Tsyganov

Publication date: 24 January 2014

Published in: Theoretical and Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11232-012-0128-0

zbMATH Keywords

integrable systemnonholonomic systemChaplygin ballVeselova system

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Groups and algebras in quantum theory and relations with integrable systems (81R12)

Related Items

Bäcklund transformations for the nonholonomic Veselova system, The geometry and integrability of the Suslov problem, Integrable discretization and deformation of the nonholonomic Chaplygin ball, On the Lie integrability theorem for the Chaplygin ball, Poisson structures for two nonholonomic systems with partially reduced symmetries, Integrability of nonholonomic Heisenberg type systems, On the Chaplygin sphere in a magnetic field, ON GENERALIZED NONHOLONOMIC CHAPLYGIN SPHERE PROBLEM, Hamiltonization and separation of variables for a Chaplygin ball on a rotating plane

Cites Work

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• Integrable Euler top and nonholonomic Chaplygin ball
• Nonholonomic Hamilton-Jacobi theory via Chaplygin Hamiltonization
• Linear almost Poisson structures and Hamilton-Jacobi equation. Applications to nonholonomic mechanics
• Hamiltonization and integrability of the Chaplygin sphere in \(\mathbb R^{n}\)
• Conservation laws, hierarchy of dynamics and explicit integration of nonholonomic systems
• Hamiltonization of the generalized Veselova LR system
• One invariant measure and different Poisson brackets for two non-holonomic systems
• Integrable nonholonomic systems on Lie groups
• Magnetic flows on homogeneous spaces
• Chaplygin systems associated to Cartan decompositions of semi-simple Lie groups
• Integrable one-particle potentials related to the Neumann system and the Jacobi problem of geodesic motion on an ellipsoid.
• Complete involutive algebras of functions on cotangent bundles of homogeneous spaces
• Chaplygin's ball rolling problem is Hamiltonian
• The Stäckel systems and algebraic curves
• INTEGRABLE CASES OF THE DYNAMICS OF A RIGID BODY, AND INTEGRABLE SYSTEMS ON THE SPHERESSⁿ