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A Geometric Characterization of Certain First Integrals for Nonholonomic Systems with Symmetries
Paula Balseiroa,
Nicola Sansonettob a Universidade Federal Fluminense, Instituto de Matemática,
Rua Mario Santos Braga S/N, 24020-140, Niteroi, Rio de Janeiro, Brazil
b Università degli Studi di Padova, Dipartimento di Matematica,
via Trieste 64, 35121 Padova, Italy
Аннотация:
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.
Ключевые слова:
nonholonomic systems; Lie group symmetries; first integrals; gauge symmetries and gauge momenta.
MSC: 70F25;
70H33;
53D20 Поступила: 29 октября 2015 г.; в окончательном варианте
12 февраля 2016 г.; опубликована
21 февраля 2016 г.
Язык публикации: английский
DOI:
10.3842/SIGMA.2016.018
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