Gauge momenta as Casimir functions of nonholonomic systems

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.

31 pages, 1 figure

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• On the dynamics of a heavy symmetric ball that rolls without sliding on a uniformly rotating surface of revolution
• Radial kinetic nonholonomic trajectories are Riemannian geodesics!