On Integrable Perturbations of Some Nonholonomic Systems
Integrable perturbations of the nonholonomic Suslov, Veselova, Chaplygin and Heisenberg problems are discussed in the framework of the classical Bertrand-Darboux method. We study the relations between the Bertrand-Darboux type equations, well studied in the holonomic case, with their nonholonomic co...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Datum: | 2015 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2015
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/147151 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | On Integrable Perturbations of Some Nonholonomic Systems / A.V. Tsiganov // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 41 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862653393611259904 |
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| author | Tsiganov, A.V. |
| author_facet | Tsiganov, A.V. |
| citation_txt | On Integrable Perturbations of Some Nonholonomic Systems / A.V. Tsiganov // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 41 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | Integrable perturbations of the nonholonomic Suslov, Veselova, Chaplygin and Heisenberg problems are discussed in the framework of the classical Bertrand-Darboux method. We study the relations between the Bertrand-Darboux type equations, well studied in the holonomic case, with their nonholonomic counterparts and apply the results to the construction of nonholonomic integrable potentials from the known potentials in the holonomic case.
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| first_indexed | 2025-12-01T23:12:35Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-147151 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-01T23:12:35Z |
| publishDate | 2015 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Tsiganov, A.V. 2019-02-13T17:44:02Z 2019-02-13T17:44:02Z 2015 On Integrable Perturbations of Some Nonholonomic Systems / A.V. Tsiganov // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 41 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 37J60; 70G45; 70H45 DOI:10.3842/SIGMA.2015.085 https://nasplib.isofts.kiev.ua/handle/123456789/147151 Integrable perturbations of the nonholonomic Suslov, Veselova, Chaplygin and Heisenberg problems are discussed in the framework of the classical Bertrand-Darboux method. We study the relations between the Bertrand-Darboux type equations, well studied in the holonomic case, with their nonholonomic counterparts and apply the results to the construction of nonholonomic integrable potentials from the known potentials in the holonomic case. 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.
 We are greatly indebted B. Jovanovi´c and the anonymous referees for a relevant contribution
 to improve the paper. The work on the revised, final version of this paper was supported by
 Russian Science Foundation (project No 15-12-20035). en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications On Integrable Perturbations of Some Nonholonomic Systems Article published earlier |
| spellingShingle | On Integrable Perturbations of Some Nonholonomic Systems Tsiganov, A.V. |
| title | On Integrable Perturbations of Some Nonholonomic Systems |
| title_full | On Integrable Perturbations of Some Nonholonomic Systems |
| title_fullStr | On Integrable Perturbations of Some Nonholonomic Systems |
| title_full_unstemmed | On Integrable Perturbations of Some Nonholonomic Systems |
| title_short | On Integrable Perturbations of Some Nonholonomic Systems |
| title_sort | on integrable perturbations of some nonholonomic systems |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147151 |
| work_keys_str_mv | AT tsiganovav onintegrableperturbationsofsomenonholonomicsystems |