Geodesic
Hamiltonisation, measure preservation and first integrals of the multi-dimensional rubber Routh sphere
Theoretical and applied mechanics, Tome 46 (2019) no. 1, p. 65

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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 García-Naranjo \cite{LGN18} and García-Naranjo and Marrero \cite{GNMarr2018}, 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.
DOI : 10.2298/TAM190130004G
Classification : 37J60, 70G45
Keywords: nonholonomic systems, Hamiltonisation, multi-dimensional rigid body dynamics, symmetries and reduction, Chaplygin systems 
Luis C. García-Naranjo. Hamiltonisation, measure preservation and first integrals of the multi-dimensional rubber Routh sphere. Theoretical and applied mechanics, Tome 46 (2019) no. 1, p. 65 . doi: 10.2298/TAM190130004G
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