Hamiltonisation, measure preservation and first integrals of the multi-dimensional rubber Routh sphere
Abstract
We consider the multi-dimensional generalisation of the problem of a sphere, with axi-symmetric mass distribution, that rolls without slipping or spinning over a plane. Using recent results from Garc\'ia-Naranjo (arXiv: 1805:06393) and Garc\'ia-Naranjo and Marrero (arXiv: 1812.01422), we show that the reduced equations of motion possess an invariant measure and may be represented in Hamiltonian form by Chaplygin's reducing multiplier method. We also prove a general result on the existence of first integrals for certain Hamiltonisable Chaplygin systems with internal symmetries that is used to determine conserved quantities of the problem.
Keywords
Cite
@article{arxiv.1901.11092,
title = {Hamiltonisation, measure preservation and first integrals of the multi-dimensional rubber Routh sphere},
author = {Luis C. García-Naranjo},
journal= {arXiv preprint arXiv:1901.11092},
year = {2019}
}
Comments
23 pages, 1 figure. Submitted to the special issue of Theor. Appl. Mech. in honour of Chaplygin's 150th anniversary