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J. Appl. Nonlinear Dyn., 2013, Volume 2, Issue 2, Pages 161–173 (Mi jand1)  

Rolling of a rigid body without slipping and spinning: kinematics and dynamics

A. V. Borisovabc, I. S. Mamaevabc, D. V. Treschevde

a Institute of Mathematics and Mechanics of the Ural Branch of RAS, S. Kovalevskaja str. 16, Ekaterinburg, 620990, Russia
b Institute of Computer Science; Laboratory of nonlinear analysis and the design of new types of vehicles, Udmurt State University Universitetskaya 1, Izhevsk, 426034 Russia
c A. A. Blagonravov Mechanical Engineering Research Institute of RAS, Bardina str. 4, Moscow, 117334, Russia
d Lomonosov Moscow State University, Leninskie Gory 1, Moscow, 119991, Russia
e Steklov Mathematical Institute, Gubkina st. 8, Moscow, 119991, Russia

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.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation 11.G34.31.0039
-2519.2012.1
1.1248.2011
14.37.21.1935


DOI: https://doi.org/10.5890/JAND.2013.04.005


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