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.
Keywords:
nonholonomic systems; Lie group symmetries; first integrals; gauge symmetries and gauge momenta.
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.
Received:October 29, 2015; in final form February 12, 2016; Published online February 21, 2016
Citation:
Paula Balseiro, Nicola Sansonetto, “A Geometric Characterization of Certain First Integrals for Nonholonomic Systems with Symmetries”, SIGMA, 12 (2016), 018, 14 pp.
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\paper A Geometric Characterization of Certain First Integrals for Nonholonomic Systems with Symmetries
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\papernumber 018
\totalpages 14
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\crossref{https://doi.org/10.3842/SIGMA.2016.018}
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