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.
Gauge Momenta as Casimir Functions of Nonholonomic Systems
Garcia-Naranjo L. C.
;
2018
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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