# American Institute of Mathematical Sciences

June  2012, 4(2): 129-136. doi: 10.3934/jgm.2012.4.129

## Linear weakly Noetherian constants of motion are horizontal gauge momenta

 1 Università di Padova, Dipartimento di Matematica Pura e Applicata, Via Trieste 63, 35121 Padova 2 Università di Verona, Dipartimento di Informatica, Cà Vignal 2, Strada Le Grazie 15, 37134 Verona

Received  October 2010 Revised  March 2011 Published  August 2012

noindent The notion of gauge momenta is a generalization of the momentum map which is relevant for nonholonomic systems with symmetry. Weakly Noetherian functions are functions which are constants of motion of all 'natural' nonholonomic systems with a given kinetic energy and any $G$-invariant potential energy. We show that, when the action of the symmetry group on the configuration manifold is free and proper, a function which is linear in the velocities is weakly-Noetherian if anf only if it is a gauge momenta which has a horizontal generator.
Citation: Francesco Fassò, Andrea Giacobbe, Nicola Sansonetto. Linear weakly Noetherian constants of motion are horizontal gauge momenta. Journal of Geometric Mechanics, 2012, 4 (2) : 129-136. doi: 10.3934/jgm.2012.4.129
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