Integrability of Nonholonomically Coupled Oscillators
Journal article, 2014

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.

reversible integrability

Lagrange D'Alembert

KAM theory

geometric integration

Continuously variable transmission

Nonholonomic mechanics


Klas Modin

Chalmers, Mathematical Sciences, Mathematics

University of Gothenburg

Olivier Verdier

University of Bergen

Discrete and Continuous Dynamical Systems

1078-0947 (ISSN)

Vol. 34 3 1121-1130

Areas of Advance

Information and Communication Technology

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Computational Mathematics



Basic sciences



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