Rolling of a rigid body on a plane and sphere. Hierarchy of dynamics
type: Item
instance of: scholarly article
title: Rolling of a rigid body on a plane and sphere. Hierarchy of dynamics
zbMATH Open document ID: 1058.70009
author: A. V. Borisov
author: I. S. Mamaev
published in: Regular and Chaotic Dynamics
publication date: 2003-02-24T00:00:00Z
review text: The authors study the existence of invariant measure, additional first integrals, and Poisson structure in the problem of a rigid body rolling without sliding on a plane or sphere. The problem of a rigid body motion on a plane was studied by S. A. Chaplygin, P. Appell, and D. Korteweg. They showed that the equations of motion are reduced to a second-order linear differential equation in the case when the surface of dynamically symmetric body is a surface of revolution. It turns out that after some change of time defined by reducing multiplier, the reduced system is a Hamiltonian system. The authors consider different cases when the integrals and invariant measure can be presented as finite algebraic expressions. They also consider a generalized problem of rolling of dynamically nonsymmetric Chaplygin ball.
Mathematics Subject Classification ID: 70E18
Mathematics Subject Classification ID: 70E40
zbMATH DE Number: 1873400
zbMATH Keywords: nonholonomic constraint
zbMATH Keywords: integral of motion
zbMATH Keywords: invariant measure
zbMATH Keywords: Poisson structure
zbMATH Keywords: Hamiltonian equations
reviewed by: I. A. Taimanov
MaRDI profile type: Publication
full work available at URL: rd2002v007n02abeh000204
OpenAlex ID: W4245664640
DOI: 10.1070/RD2002V007N02ABEH000204
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description: scientific article; zbMATH DE number 1873400