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

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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.
Keywords: nonholonomic systems, Hamiltonisation, multi-dimensional rigid body dynamics, symmetries and reduction, Chaplygin systems 
@article{TAM_2019_46_1_a5,
     author = {Luis C. Garc{\'\i}a-Naranjo},
     title = {Hamiltonisation, measure preservation and first integrals of the multi-dimensional rubber {Routh} sphere},
     journal = {Theoretical and applied mechanics},
     pages = {65 - 88},
     publisher = {mathdoc},
     volume = {46},
     number = {1},
     year = {2019},
     url = {http://geodesic.mathdoc.fr/item/TAM_2019_46_1_a5/}
}
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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. http://geodesic.mathdoc.fr/item/TAM_2019_46_1_a5/