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Integrability of Nonholonomically Coupled Oscillators

Journal article
Authors Klas Modin
Olivier Verdier
Published in Discrete and Continuous Dynamical Systems. Series A
Volume 34
Issue 3
Pages 1121-1130
ISSN 1078-0947
Publication year 2014
Published at Department of Mathematical Sciences, Mathematics
Pages 1121-1130
Language en
Links dx.doi.org/10.3934/dcds.2014.34.112...
Keywords Nonholonomic mechanics, Lagrange D'Alembert, Continuously variable transmission, reversible integrability, KAM theory, geometric integration
Subject categories Geometry, Numerical analysis

Abstract

We study a family of nonholonomic mechanical systems. These systems consist of harmonic oscillators coupled through nonholonomic constraints. In particular, the family includes the so called contact oscillator, which has been used as a test problem for numerical methods for nonholonomic mechanics. Furthermore, the systems under study constitute simple models for continuously variable transmission gearboxes. The main result is that each system in the family is integrable reversible with respect to the canonical reversibility map on the cotangent bundle. This result may explain previous numerical observations, that some discretisations of the contact oscillator have favourable structure preserving properties.

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