A Geometric Characterization of Certain First Integrals for Nonholonomic Systems with Symmetries

Домашня сторінка
→
Фізико-технічні та математичні науки
→
Відділення математики
→
Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
→
Symmetry, Integrability and Geometry: Methods and Applications, 2016, том 12
→
Symmetry, Integrability and Geometry: Methods and Applications, 2016, том 12, випуск за цей рік
→
Переглянути статтю

dc.contributor.author	Balseiro, P.
dc.contributor.author	Sansonetto, N.
dc.date.accessioned	2019-02-14T18:32:10Z
dc.date.available	2019-02-14T18:32:10Z
dc.date.issued	2016
dc.identifier.citation	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.	uk_UA
dc.identifier.issn	1815-0659
dc.identifier.other	2010 Mathematics Subject Classification: 70F25; 70H33; 53D20
dc.identifier.other	DOI:10.3842/SIGMA.2016.018
dc.identifier.uri	http://dspace.nbuv.gov.ua/handle/123456789/147431
dc.description.abstract	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.	uk_UA
dc.description.sponsorship	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.	uk_UA
dc.language.iso	en	uk_UA
dc.publisher	Інститут математики НАН України	uk_UA
dc.relation.ispartof	Symmetry, Integrability and Geometry: Methods and Applications
dc.title	A Geometric Characterization of Certain First Integrals for Nonholonomic Systems with Symmetries	uk_UA
dc.type	Article	uk_UA
dc.status	published earlier	uk_UA