Variational integrators for hamiltonizable nonholonomic systems
type: Item
instance of: scholarly article
title: Variational integrators for hamiltonizable nonholonomic systems
zbMATH Open document ID: 1262.65193
author: O. E. Fernandez
author: Anthony M. Bloch
author: Peter J. Olver
published in: Journal of Geometric Mechanics
publication date: 2012-11-15T00:00:00Z
review text: The authors study the design of variational integrators for a certain class of nonholonomic systems. By definition, nonholonomic systems do not possess a variational structure. However, already Chaplygin showed that in certain special cases, suitable time reparametrizations lead to a Hamiltonian form. In this article, the authors consider the Poincaré and the Sundman transformations which have already been much used in the context of symplectic integrators with adaptive step sizes. They design two types of variational integrators for Hamiltonizable Chaplygin systems and apply them to three different examples. The results seem to indicate a superior long-time behaviour compared with standard nonholonomic integrators.
reviewed by: Werner M. Seiler
Mathematics Subject Classification ID: 65P10
Mathematics Subject Classification ID: 37J60
Mathematics Subject Classification ID: 70F25
Mathematics Subject Classification ID: 70H45
zbMATH DE Number: 6107611
zbMATH Keywords: nonholonomic system
zbMATH Keywords: Chaplygin system
zbMATH Keywords: variational integrator
zbMATH Keywords: Hamiltonization
MaRDI profile type: Publication
full work available at URL: jgm.2012.4.137
OpenAlex ID: W2329610818
DOI: 10.3934/JGM.2012.4.137
describes a project that uses: Digital Library of Mathematical Functions
description: scientific article; zbMATH DE number 6107611