Gauge momenta as Casimir functions of nonholonomic systems

Luis C. García-Naranjo, James Montaldi

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    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 languageEnglish
    Pages (from-to)563–602
    Number of pages40
    JournalArchive for Rational Mechanics and Analysis
    Issue number0
    Early online date29 Nov 2017
    Publication statusPublished - 2 Dec 2017


    • Symmetric systems
    • nonholonomic constraints
    • Poisson structures


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