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Integrability of Nonholonomically Coupled Oscillators

Klas Modin (Institutionen för matematiska vetenskaper, matematik) ; Olivier Verdier
Discrete and Continuous Dynamical Systems. Series A (1078-0947). Vol. 34 (2014), 3, p. 1121-1130.
[Artikel, refereegranskad vetenskaplig]

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.

Nyckelord: Nonholonomic mechanics, Lagrange D'Alembert, Continuously variable transmission, reversible integrability, KAM theory, geometric integration

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Denna post skapades 2013-07-23. Senast ändrad 2015-03-03.
CPL Pubid: 180252


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