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Nelin. Dinam., 2012, Volume 8, Number 4, Pages 783–797 (Mi nd360)  

This article is cited in 4 scientific papers (total in 4 papers)

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

Alexey V. Borisovabc, Ivan S. Mamaevabc, Dmitrii V. Treschevde

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

Keywords: rolling without slipping, nonholonomic constraint, Chaplygin system, conformally Hamiltonian system

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

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English version:
J. Appl. Nonlinear Dyn., 2013, 2:2, 161–173

UDC: 517.925
MSC: 37J60, 37J35
Received: 06.09.2012
Revised: 28.11.2012

Citation: Alexey V. Borisov, Ivan S. Mamaev, Dmitrii V. Treschev, “Rolling of a rigid body without slipping and spinning: kinematics and dynamics”, Nelin. Dinam., 8:4 (2012), 783–797; J. Appl. Nonlinear Dyn., 2:2 (2013), 161–173

Citation in format AMSBIB
\by Alexey~V.~Borisov, Ivan~S.~Mamaev, Dmitrii~V.~Treschev
\paper Rolling of a rigid body without slipping and spinning: kinematics and dynamics
\jour Nelin. Dinam.
\yr 2012
\vol 8
\issue 4
\pages 783--797
\jour J. Appl. Nonlinear Dyn.
\yr 2013
\vol 2
\issue 2
\pages 161--173

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    This publication is cited in the following articles:
    1. A. V. Bolsinov, A. V. Borisov, I. S. Mamaev, “Kachenie bez vercheniya shara po ploskosti: otsutstvie invariantnoi mery v sisteme s polnym naborom integralov”, Nelineinaya dinam., 8:3 (2012), 605–616  mathnet
    2. A. V. Borisov, I. S. Mamaev, I. A. Bizyaev, “Ierarkhiya dinamiki pri kachenii tverdogo tela bez proskalzyvaniya i vercheniya po ploskosti i sfere”, Nelineinaya dinam., 9:2 (2013), 141–202  mathnet
    3. I. A. Bizyaev, A. V. Borisov, I. S. Mamaev, “Dinamika negolonomnykh sistem, sostoyaschikh iz sfericheskoi obolochki s podvizhnym tverdym telom vnutri”, Nelineinaya dinam., 9:3 (2013), 547–566  mathnet
    4. Bizyaev I.A., Borisov A.V., Mamaev I.S., “The Dynamics of Nonholonomic Systems Consisting of a Spherical Shell With a Moving Rigid Body Inside”, Regul. Chaotic Dyn., 19:2 (2014), 198–213  crossref  isi
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