Geodesic
The hierarchy of dynamics of a rigid body rolling without slipping and spinning on a plane and a sphere
Russian journal of nonlinear dynamics, Tome 9 (2013) no. 2, pp. 141-202

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In this paper, we investigate the dynamics of systems describing the rolling without slipping and spinning (rubber rolling) of various rigid bodies on a plane and a sphere. It is shown that a hierarchy of possible types of dynamical behavior arises depending on the body’s surface geometry and mass distribution. New integrable cases and cases of existence of an invariant measure are found. In addition, these systems are used to illustrate that the existence of several nontrivial involutions in reversible dissipative systems leads to quasi-Hamiltonian behavior.
Keywords: nonholonomic constraint, tensor invariant, first integral, invariant measure, integrability, conformally Hamiltonian system, rubber rolling, involution.
Mots-clés : reversible 
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Alexey V. Borisov; Ivan S. Mamaev; Ivan A. Bizyaev. The hierarchy of dynamics of a rigid body rolling without slipping and spinning on a plane and a sphere. Russian journal of nonlinear dynamics, Tome 9 (2013) no. 2, pp. 141-202. http://geodesic.mathdoc.fr/item/ND_2013_9_2_a0/