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A Geometric Characterization of Certain First Integrals for Nonholonomic Systems with Symmetries
Symmetry, integrability and geometry: methods and applications, Tome 12 (2016) Cet article a éte moissonné depuis la source Math-Net.Ru

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We study the existence of first integrals in nonholonomic systems with symmetry. First we define the concept of $\mathcal{M}$-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. 
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     title = {A {Geometric} {Characterization} of {Certain} {First} {Integrals} for {Nonholonomic} {Systems} with {Symmetries}},
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}
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Paula Balseiro; Nicola Sansonetto. A Geometric Characterization of Certain First Integrals for Nonholonomic Systems with Symmetries. Symmetry, integrability and geometry: methods and applications, Tome 12 (2016). http://geodesic.mathdoc.fr/item/SIGMA_2016_12_a17/

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