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SIGMA, 2016, Volume 12, 112, 14 pages (Mi sigma1194)  

This article is cited in 2 scientific papers (total in 2 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

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


DOI: https://doi.org/10.3842/SIGMA.2016.112

Full text: PDF file (340 kB)
Full text: http://www.emis.de/journals/SIGMA/2016/112/
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Bibliographic databases:

ArXiv: 1603.03528
MSC: 37J60; 70G45; 70H45
Received: March 17, 2016; in final form November 22, 2016; Published online November 25, 2016
Language:

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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\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
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\crossref{https://doi.org/10.3842/SIGMA.2016.112}
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\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85014858075}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Tsiganov A.V., “Backlund Transformations and New Integrable Systems on the Plane”, Springer Proceedings in Mathematics and Statistics, 273, 2018, 47-74  crossref
    2. Tsiganov A.V., “Hamiltonization and Separation of Variables For a Chaplygin Ball on a Rotating Plane”, Regul. Chaotic Dyn., 24:2 (2019), 171–186  mathnet  crossref  mathscinet  isi  scopus
  • Symmetry, Integrability and Geometry: Methods and Applications
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