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Gauge Momenta as Casimir Functions of Nonholonomic Systems

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Abstract

We consider nonholonomic systems with symmetry possessing a certain type of first integral which is 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.

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Author information

Authors and Affiliations

  1. Departamento de Matemáticas y Mecánica, IIMAS, UNAM, Apdo. Postal 20-126, Col. San Ángel, Mexico City, 01000, Mexico

    Luis C. García-Naranjo

  2. School of Mathematics, University of Manchester, Manchester, M13 9PL, UK

    James Montaldi

Authors
  1. Luis C. García-Naranjo
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  2. James Montaldi
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Correspondence to Luis C. García-Naranjo.

Additional information

Communicated by M. Ortiz

This research was made possible by a Newton Advanced Fellowship from the Royal Society.

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García-Naranjo, L.C., Montaldi, J. Gauge Momenta as Casimir Functions of Nonholonomic Systems. Arch Rational Mech Anal 228, 563–602 (2018). https://doi.org/10.1007/s00205-017-1200-6

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