Linear weakly Noetherian constants of motion        are horizontal gauge momenta

Francesco Fassò; Andrea Giacobbe; Nicola Sansonetto

doi:10.3934/jgm.2012.4.129

Article Contents

2012, Volume 4, Issue 2: 129-136. Doi: 10.3934/jgm.2012.4.129

This issue Previous Article Symmetries and reduction of multiplicative 2-forms Next Article Variational Integrators for Hamiltonizable Nonholonomic Systems

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: September 30, 2010

Revised: February 28, 2011

Published: May 2012

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Abstract

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.

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Mathematics Subject Classification: 37J15, 37J05, 70F25.

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