A Geometric Characterization of Certain First Integrals for Nonholonomic Systems with Symmetries
We study the existence of first integrals in nonholonomic systems with symmetry. First we define the concept of M-cotangent lift of a vector field on a manifold Q in order to unify the works [Balseiro P., Arch. Ration. Mech. Anal. 214 (2014), 453-501, arXiv:1301.1091], [Fassò F., Ramos A., Sansonett...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2016 |
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Інститут математики НАН України
2016
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/147431 |
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| Zitieren: | A Geometric Characterization of Certain First Integrals for Nonholonomic Systems with Symmetries / P. Balseiro, N. Sansonetto // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 35 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862636333672955904 |
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| author | Balseiro, P. Sansonetto, N. |
| author_facet | Balseiro, P. Sansonetto, N. |
| citation_txt | A Geometric Characterization of Certain First Integrals for Nonholonomic Systems with Symmetries / P. Balseiro, N. Sansonetto // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 35 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We study the existence of first integrals in nonholonomic systems with symmetry. First we define the concept of M-cotangent lift of a vector field on a manifold Q in order to unify the works [Balseiro P., Arch. Ration. Mech. Anal. 214 (2014), 453-501, arXiv:1301.1091], [Fassò F., Ramos A., Sansonetto N., Regul. Chaotic Dyn. 12 (2007), 579-588], and [Fassò F., Giacobbe A., Sansonetto N., Rep. Math. Phys. 62 (2008), 345-367]. Second, we study gauge symmetries and gauge momenta, in the cases in which there are the symmetries that satisfy the so-called vertical symmetry condition. Under such condition we can predict the number of linearly independent first integrals (that are gauge momenta). We illustrate the theory with two examples.
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| first_indexed | 2025-11-30T20:59:56Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-147431 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-30T20:59:56Z |
| publishDate | 2016 |
| publisher | Інститут математики НАН України |
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| spelling | Balseiro, P. Sansonetto, N. 2019-02-14T18:32:10Z 2019-02-14T18:32:10Z 2016 A Geometric Characterization of Certain First Integrals for Nonholonomic Systems with Symmetries / P. Balseiro, N. Sansonetto // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 35 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 70F25; 70H33; 53D20 DOI:10.3842/SIGMA.2016.018 https://nasplib.isofts.kiev.ua/handle/123456789/147431 We study the existence of first integrals in nonholonomic systems with symmetry. First we define the concept of M-cotangent lift of a vector field on a manifold Q in order to unify the works [Balseiro P., Arch. Ration. Mech. Anal. 214 (2014), 453-501, arXiv:1301.1091], [Fassò F., Ramos A., Sansonetto N., Regul. Chaotic Dyn. 12 (2007), 579-588], and [Fassò F., Giacobbe A., Sansonetto N., Rep. Math. Phys. 62 (2008), 345-367]. Second, we study gauge symmetries and gauge momenta, in the cases in which there are the symmetries that satisfy the so-called vertical symmetry condition. Under such condition we can predict the number of linearly independent first integrals (that are gauge momenta). We illustrate the theory with two examples. 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.
 This work is partially supported by the research projects Symmetries and integrability of nonholonomic
 mechanical systems of the University of Padova. N.S. wishes to thank IMPA and
 H. Bursztyn for the kind hospitality during which this work took origin. P.B. thanks the financial
 support of CAPES (grants PVE 11/2012 and PVE 089/2013) and CNPq’s Universal grant. We
 also thank the anonymous referees for their useful comment. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications A Geometric Characterization of Certain First Integrals for Nonholonomic Systems with Symmetries Article published earlier |
| spellingShingle | A Geometric Characterization of Certain First Integrals for Nonholonomic Systems with Symmetries Balseiro, P. Sansonetto, N. |
| title | A Geometric Characterization of Certain First Integrals for Nonholonomic Systems with Symmetries |
| title_full | A Geometric Characterization of Certain First Integrals for Nonholonomic Systems with Symmetries |
| title_fullStr | A Geometric Characterization of Certain First Integrals for Nonholonomic Systems with Symmetries |
| title_full_unstemmed | A Geometric Characterization of Certain First Integrals for Nonholonomic Systems with Symmetries |
| title_short | A Geometric Characterization of Certain First Integrals for Nonholonomic Systems with Symmetries |
| title_sort | geometric characterization of certain first integrals for nonholonomic systems with symmetries |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147431 |
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