Abstract:
We show that some modern geometric methods of Hamiltonian dynamics can be directly applied to the nonholonomic Heisenberg type systems. As an example we present characteristic Killing tensors, compatible Poisson brackets, Lax matrices and classical $r$-matrices for the conformally Hamiltonian vector fields obtained in a process of reduction of Hamiltonian vector fields by a nonholonomic constraint associated with the Heisenberg system.
Citation:
Yury A. Grigoryev, Alexey P. Sozonov, Andrey V. Tsiganov, “Integrability of Nonholonomic Heisenberg Type Systems”, SIGMA, 12 (2016), 112, 14 pp.
\Bibitem{GriSozTsi16}
\by Yury~A.~Grigoryev, Alexey~P.~Sozonov, Andrey~V.~Tsiganov
\paper Integrability of Nonholonomic Heisenberg Type Systems
\jour SIGMA
\yr 2016
\vol 12
\papernumber 112
\totalpages 14
\mathnet{http://mi.mathnet.ru/sigma1194}
\crossref{https://doi.org/10.3842/SIGMA.2016.112}
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Linking options:
https://www.mathnet.ru/eng/sigma1194
https://www.mathnet.ru/eng/sigma/v12/p112
This publication is cited in the following 3 articles:
A. V. Tsiganov, “On a time-dependent nonholonomic oscillator”, Russ. J. Math. Phys., 27:3 (2020), 399–409
Andrey V. Tsiganov, “Hamiltonization and Separation of Variables for a Chaplygin Ball on a Rotating Plane”, Regul. Chaotic Dyn., 24:2 (2019), 171–186
Tsiganov A.V., “Backlund Transformations and New Integrable Systems on the Plane”, Springer Proceedings in Mathematics and Statistics, 273, 2018, 47-74
Citation in format AMSBIB
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