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Symmetry, Integrability and Geometry: Methods and Applications, 2016, Volume 12, 112, 14 pp.
DOI: https://doi.org/10.3842/SIGMA.2016.112 (Mi sigma1194) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Integrability of Nonholonomic Heisenberg Type Systems

Yury A. Grigoryeva, Alexey P. Sozonova, Andrey V. Tsiganovba

a St. Petersburg State University, St. Petersburg, Russia
b Udmurt State University, Izhevsk, Russia
Full-text PDF (340 kB) Citations (3)
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DOI: https://doi.org/10.3842/SIGMA.2016.112
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.
Keywords: Hamiltonian dynamics; nonholonomic systems.
Funding agency Grant number
Russian Science Foundation 15-12-20035
15-11-30007
Received: March 17, 2016; in final form November 22, 2016; Published online November 25, 2016
Bibliographic databases:
Document Type: Article
MSC: 37J60; 70G45; 70H45
Language: English
Citation: Yury A. Grigoryev, Alexey P. Sozonov, Andrey V. Tsiganov, “Integrability of Nonholonomic Heisenberg Type Systems”, SIGMA, 12 (2016), 112, 14 pp.
Citation in format AMSBIB
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Symmetry, Integrability and Geometry: Methods and Applications
     
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