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arXiv · 1901.11092

Hamiltonisation, measure preservation and first integrals of the multi-dimensional rubber Routh sphere

Luis C. García-Naranjo
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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.

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Luis C. García-Naranjo. 2019-01-30. Hamiltonisation, measure preservation and first integrals of the multi-dimensional rubber Routh sphere. https://doi.org/10.2298/tam190130004g

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