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Integrability of Nonholonomic Heisenberg Type Systems
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- Фізико-технічні та математичні науки
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- Відділення математики
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2016, том 12
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Integrability of Nonholonomic Heisenberg Type Systems
Інший ID:
2010 Mathematics Subject Classification: 37J60; 70G45; 70H45
DOI:10.3842/SIGMA.2016.112
DOI:10.3842/SIGMA.2016.112
Посилання:
Integrability of Nonholonomic Heisenberg Type Systems / Y. A. Grigoryev, A.P. Sozonov, A.V. Tsiganov // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 25 назв. — англ.
Підтримка:
We are very grateful to the referees for thorough analysis of the manuscript, constructive suggestions
and proposed corrections, which certainly lead to a more profound discussion of the
results. We are also deeply grateful A.V. Borisov and I.A. Bizayev for the relevant discussion. Section 2 was written by A.V. Tsiganov and supported by the Russian Science Foundation
(project 15-12-20035). Section 3 was written by Yu.A. Grigoryev and A.P. Sozonov within the
framework of the Russian Science Foundation (project 15-11-30007).
Дата:
2016
Переглядів:
448
Завантажень:
234
Анотація:
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.
