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Journal of Applied Nonlinear Dynamics 2(2) (2013) 161--173 | DOI:10.5890/JAND.2013.04.005

A.V. Borisov$^{1}$, I.S. Mamaev$^{2}$, D.V. Treschev$^{2}$,$^{3}$

$^{1}$ Laboratory of Nonlinear Analysis and the Design of New Types of Vehicles,Udmurt State University, Universitetskaya 1, Izhevsk, 426034 Russia

$^{2}$ Lomonosov Moscow State University, Leninskie Gory 1, Moscow, 119991, Russia

$^{3}$ Steklov Mathematical Institute, Gubkina st. 8, Moscow, 119991, Russia

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Abstract

In this paper we investigate various kinematic properties of rolling of one rigid body on another both for the classical model of rolling without slipping (the velocities of bodies at the point of contact coincide) and for the model of rubber-rolling (with the additional condition that the spinning of the bodies relative to each other be excluded). Furthermore, in the case where both bodies are bounded by spherical surfaces and one of them is fixed, the equations of motion for a moving ball are represented in the form of the Chaplygin system. When the center of mass of the moving ball coincides with its geometric center, the equations of motion are represented in conformally Hamiltonian form, and in the case where the radii of the moving and fixed spheres coincides, they are written in Hamiltonian form.

Acknowledgments

This research was done at the Udmurt State University and was supported by the Grant Program of the Government of the Russian Federation for state support of scientific research conducted under the supervision of leading scientists at Russian institutions of higher professional education (Contract No11.G34.31.0039). The study was supported by the Ministry of education and science of Russian Federation, project 14.B37.21.1935.

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