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A Geometric Characterization of Certain First Integrals for Nonholonomic Systems with Symmetries
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2016, том 12
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A Geometric Characterization of Certain First Integrals for Nonholonomic Systems with Symmetries
Інший ID:
2010 Mathematics Subject Classification: 70F25; 70H33; 53D20
DOI:10.3842/SIGMA.2016.018
DOI:10.3842/SIGMA.2016.018
Посилання:
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.
Підтримка:
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.
Дата:
2016
Переглядів:
760
Завантажень:
304
Анотація:
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.
