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Integrability of Nonholonomically Coupled Oscillators
Department of Mathematical Sciences, Chalmers University of Technology, Sweden.
Department of Mathematics, University of Bergen, Norway.
2014 (English)In: Discrete and Continuous Dynamical Systems, ISSN 1078-0947, E-ISSN 1553-5231, Vol. 34, no 3, 1121-1130 p.Article in journal (Refereed) Epub ahead of print
Abstract [en]

We study a family of nonholonomic mechanical systems. These systems consist of harmonic oscillators coupled through nonholonomic constraints. The family includes the contact oscillator, which has been used as a test problem for numerical methods for nonholonomic mechanics. 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. By using reversible Kolmogorov--Arnold--Moser theory, we then establish preservation of invariant tori for reversible perturbations. This result explains previous numerical observations, that some discretisations of the contact oscillator have favourable structure preserving properties.

Place, publisher, year, edition, pages
American Institute of Mathematical Sciences, 2014. Vol. 34, no 3, 1121-1130 p.
Keyword [en]
Nonholonomic mechanics, Lagrange D'Alembert, Continuously variable transmission, reversible integrability, KAM theory, geometric integration
National Category
Computational Mathematics
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:umu:diva-79402DOI: 10.3934/dcds.2014.34.1121OAI: oai:DiVA.org:umu-79402DiVA: diva2:641403
Note

Published online August 2013.

Available from: 2013-08-16 Created: 2013-08-16 Last updated: 2017-12-06Bibliographically approved

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Verdier, Olivier
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