Gauge momenta as Casimir functions of nonholonomic systems

Luis C. García-Naranjo; James Montaldi

doi:10.1007/s00205-017-1200-6

Gauge momenta as Casimir functions of nonholonomic systems

Luis C. García-Naranjo, James Montaldi

IIMAS, Universidad Autonoma de Mexico

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Abstract

We consider nonholonomic systems with symmetry possessing a certain type of first integrals that are linear in the velocities. We develop a systematic method for modifying the standard nonholonomic almost Poisson structure that describes the dynamics so that these integrals become Casimir functions after reduction. This explains a number of recent results on Hamiltonization of nonholonomic systems, and has consequences for the study of relative equilibria in such systems.

Original language	English
Pages (from-to)	563–602
Number of pages	40
Journal	Archive for Rational Mechanics and Analysis
Volume	228
Issue number	0
Early online date	29 Nov 2017
DOIs	https://doi.org/10.1007/s00205-017-1200-6
Publication status	Published - 2 Dec 2017

Keywords

Symmetric systems
nonholonomic constraints
Poisson structures

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10.1007/s00205-017-1200-6

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AB - We consider nonholonomic systems with symmetry possessing a certain type of first integrals that are linear in the velocities. We develop a systematic method for modifying the standard nonholonomic almost Poisson structure that describes the dynamics so that these integrals become Casimir functions after reduction. This explains a number of recent results on Hamiltonization of nonholonomic systems, and has consequences for the study of relative equilibria in such systems.

KW - Symmetric systems

KW - nonholonomic constraints

KW - Poisson structures

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Gauge momenta as Casimir functions of nonholonomic systems

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Keywords

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