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.

reversible integrability

Lagrange D'Alembert

KAM theory

geometric integration

Continuously variable transmission

Nonholonomic mechanics

Författare

Klas Modin

Chalmers, Matematiska vetenskaper, Matematik

Göteborgs universitet

Olivier Verdier

Universitetet i Bergen

Discrete and Continuous Dynamical Systems

1078-0947 (ISSN)

Vol. 34 3 1121-1130

Styrkeområden

Informations- och kommunikationsteknik

Ämneskategorier

Beräkningsmatematik

Geometri

Fundament

Grundläggande vetenskaper

DOI

10.3934/dcds.2014.34.1121

Mer information

Senast uppdaterat

2020-02-03