Precession and recession of the rock'n'roller

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Title: Precession and recession of the rock'n'roller
Authors: Lynch, Peter
Bustamante, Miguel
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Date: 30-Sep-2009
Online since: 2011-04-08T11:10:13Z
Abstract: We study the dynamics of a spherical rigid body that rocks and rolls on a plane under the effect of gravity. The distribution of mass is non-uniform and the centre of mass does not coincide with the geometric centre. The symmetric case, with moments of inertia I1 = I2 < I3, is integrable and themotion is completely regular. Three known conservation laws are the total energy E, Jellett’s quantity QJ and Routh’s quantity QR. When the inertial symmetry I1 = I2 is broken, even slightly, the character of the solutions is profoundly changed and new types of motion become possible. We derive the equations governing the general motion and present analytical and numerical evidence of the recession, or reversal of precession, that has been observed in physical experiments. We present an analysis of recession in terms of critical lines dividing the (QR,QJ ) plane into four dynamically disjoint zones. We prove that recession implies the lack of conservation of Jellett’s and Routh’s quantities, by identifying individual reversals as crossings of the orbit (QR(t ),QJ (t)) through the critical lines. Consequently, a method is found to produce a large number of initial conditions so that the system will exhibit recession.
Funding Details: Not applicable
Type of material: Journal Article
Publisher: IOP Publishing
Journal: Journal of Physics A: Mathematical and Theoretical
Volume: 42
Issue: 42
Start page: 425203 (25pp)
Copyright (published version): 2009 IOP Publishing Ltd
Keywords: Rigid body dynamics
Subject LCSH: Rotational motion (Rigid dynamics)
Hamiltonian systems
DOI: 10.1088/1751-8113/42/42/425203
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Language: en
Status of Item: Peer reviewed
Appears in Collections:Mathematics and Statistics Research Collection

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