Integrability of Nonholonomically Coupled Oscillators
Provides a theoretical explanation for numerical observations in nonholonomic mechanics, relevant to researchers studying geometric integration and mechanical systems with constraints.
The paper proves that a family of nonholonomically coupled harmonic oscillators, including the contact oscillator, is integrable and reversible with respect to the canonical reversibility map. This result explains previous numerical observations of favorable structure-preserving properties in discretizations of the contact oscillator.
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.