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.

Nonholonomic mechanics

reversible integrability

geometric integration

Lagrange D'Alembert

KAM theory

Continuously variable transmission

Author

Klas Modin

University of Gothenburg

Chalmers, Mathematical Sciences, Mathematics

Olivier Verdier

Discrete and Continuous Dynamical Systems

1078-0947 (ISSN)

Vol. 34 3 1121-1130

Areas of Advance

Information and Communication Technology

Subject Categories

Computational Mathematics

Geometry

Roots

Basic sciences

DOI

10.3934/dcds.2014.34.1121

More information

Created

10/8/2017