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

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
Document Type: Article
MSC: 37J60; 70G45; 70H45
Received: March 17, 2016; in final form November 22, 2016; Published online November 25, 2016
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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\paper Integrability of Nonholonomic Heisenberg Type Systems
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\papernumber 112
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