Integrability of Nonholonomically Coupled Oscillators
Artikel i vetenskaplig tidskrift, 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

Författare

Klas Modin

Göteborgs universitet

Chalmers, Matematiska vetenskaper, Matematik

Olivier Verdier

Discrete and Continuous Dynamical Systems

1078-0947 (ISSN)

Vol. 34 1121-1130

Styrkeområden

Informations- och kommunikationsteknik

Ämneskategorier

Beräkningsmatematik

Geometri

Fundament

Grundläggande vetenskaper

DOI

10.3934/dcds.2014.34.1121