The Hojman Construction and Hamiltonization of Nonholonomic Systems

In this paper, using the Hojman construction, we give examples of various Poisson brackets which differ from those which are usually analyzed in Hamiltonian mechanics. They possess a nonmaximal rank, and in the general case an invariant measure and Casimir functions can be globally absent for them.

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Published in:Symmetry, Integrability and Geometry: Methods and Applications
Date:2016
Main Authors: Bizyaev, I.A., Borisov, A.V., Mamaev, I.S.
Format: Article
Language:English
Published: Інститут математики НАН України 2016
Online Access:https://nasplib.isofts.kiev.ua/handle/123456789/147435
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Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this:The Hojman Construction and Hamiltonization of Nonholonomic Systems / I.A. Bizyaev, A.V. Borisov, I.S. Mamaev // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 41 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
id nasplib_isofts_kiev_ua-123456789-147435
record_format dspace
spelling Bizyaev, I.A.
Borisov, A.V.
Mamaev, I.S.
2019-02-14T18:34:02Z
2019-02-14T18:34:02Z
2016
The Hojman Construction and Hamiltonization of Nonholonomic Systems / I.A. Bizyaev, A.V. Borisov, I.S. Mamaev // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 41 назв. — англ.
1815-0659
2010 Mathematics Subject Classification: 37J60; 37J05
DOI:10.3842/SIGMA.2016.012
https://nasplib.isofts.kiev.ua/handle/123456789/147435
In this paper, using the Hojman construction, we give examples of various Poisson brackets which differ from those which are usually analyzed in Hamiltonian mechanics. They possess a nonmaximal rank, and in the general case an invariant measure and Casimir functions can be globally absent for them.
This paper is a contribution to the Special Issue on Analytical Mechanics and Dif ferential Geometry in honour of Sergio Benenti. The full collection is available at http://www.emis.de/journals/SIGMA/Benenti.html. Section 3 was prepared by A.V. Borisov under the RSF grant No. 15-12-20035. Section 2 was written by I.S. Mamaev within the framework of the state assignment for institutions of higher education. The work of I.A. Bizyaev (Sections 4 and 5) was supported by RFBR grant No. 15- 31-50172. The authors thank A.V. Tsiganov and A.V. Bolsinov for useful discussions and the referees for numerous comments, which have contributed to the improvement of this paper.
en
Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
The Hojman Construction and Hamiltonization of Nonholonomic Systems
Article
published earlier
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
title The Hojman Construction and Hamiltonization of Nonholonomic Systems
spellingShingle The Hojman Construction and Hamiltonization of Nonholonomic Systems
Bizyaev, I.A.
Borisov, A.V.
Mamaev, I.S.
title_short The Hojman Construction and Hamiltonization of Nonholonomic Systems
title_full The Hojman Construction and Hamiltonization of Nonholonomic Systems
title_fullStr The Hojman Construction and Hamiltonization of Nonholonomic Systems
title_full_unstemmed The Hojman Construction and Hamiltonization of Nonholonomic Systems
title_sort hojman construction and hamiltonization of nonholonomic systems
author Bizyaev, I.A.
Borisov, A.V.
Mamaev, I.S.
author_facet Bizyaev, I.A.
Borisov, A.V.
Mamaev, I.S.
publishDate 2016
language English
container_title Symmetry, Integrability and Geometry: Methods and Applications
publisher Інститут математики НАН України
format Article
description In this paper, using the Hojman construction, we give examples of various Poisson brackets which differ from those which are usually analyzed in Hamiltonian mechanics. They possess a nonmaximal rank, and in the general case an invariant measure and Casimir functions can be globally absent for them.
issn 1815-0659
url https://nasplib.isofts.kiev.ua/handle/123456789/147435
citation_txt The Hojman Construction and Hamiltonization of Nonholonomic Systems / I.A. Bizyaev, A.V. Borisov, I.S. Mamaev // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 41 назв. — англ.
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first_indexed 2025-12-07T17:56:07Z
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