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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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2016 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2016
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/147435 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | 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| _version_ | 1862715083700830208 |
|---|---|
| author | Bizyaev, I.A. Borisov, A.V. Mamaev, I.S. |
| author_facet | Bizyaev, I.A. Borisov, A.V. Mamaev, I.S. |
| 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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.
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| first_indexed | 2025-12-07T17:56:07Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-147435 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T17:56:07Z |
| publishDate | 2016 |
| publisher | Інститут математики НАН України |
| 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 |
| spellingShingle | The Hojman Construction and Hamiltonization of Nonholonomic Systems Bizyaev, I.A. Borisov, A.V. Mamaev, I.S. |
| title | 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_short | The Hojman Construction and Hamiltonization of Nonholonomic Systems |
| title_sort | hojman construction and hamiltonization of nonholonomic systems |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147435 |
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