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The hierarchy of dynamics of a rigid body rolling without slipping and spinning on a plane and a sphere |
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| Authors: | Alexey V Borisov Ivan S Mamaev Ivan A Bizyaev |
| Institution: | 1. Institute of Computer Science, Laboratory of Nonlinear Analysis and the Design of New Types of Vehicles Udmurt State University, Universitetskaya 1, Izhevsk, 426034, Russia 2. A.A. Blagonravov Mechanical Engineering Research Institute of RAS, Bardina str. 4, Moscow, 117334, Russia 3. Institute of Mathematics and Mechanics of the Ural Branch of RAS, S. Kovalevskaja str. 16, Ekaterinburg, 620990, Russia |
| Abstract: | 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. |
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