Variational Integrators for Hamiltonizable Nonholonomic Systems

Oscar E. Fernandez; Anthony M. Bloch; P. J. Olver

doi:10.3934/jgm.2012.4.137

Article Contents

2012, Volume 4, Issue 2: 137-163. Doi: 10.3934/jgm.2012.4.137

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Variational Integrators for Hamiltonizable Nonholonomic Systems

1.
Department of Mathematics, Wellesley College, Wellesley, MA 02482
2.
Department of Mathematics, University of Michigan, Ann Arbor, MI 48109
3.
School of Mathematics, University of Minnesota, Minneapolis, MN 55455

Received: April 30, 2011

Revised: September 30, 2011

Published: May 2012

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Abstract

We report on new applications of the Poincaré and Sundman time-transformations to the simulation of nonholonomic systems. These transformations are here applied to nonholonomic mechanical systems known to be Hamiltonizable (briefly, nonholonomic systems whose constrained mechanics are Hamiltonian after a suitable time reparameterization). We show how such an application permits the usage of variational integrators for these non-variational mechanical systems. Examples are given and numerical results are compared to the standard nonholonomic integrator results.

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Mathematics Subject Classification: Primary: 37J60; Secondary: 34K28.

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