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  5. Precession and recession of the rock'n'roller
 
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Precession and recession of the rock'n'roller

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Download RnR-lync0708.pdf814.81 KB
Author(s)
Lynch, Peter 
Bustamante, Miguel 
Uri
http://hdl.handle.net/10197/2893
Date Issued
30 September 2009
Date Available
08T11:10:13Z April 2011
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.
Sponsorship
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
Precession
DOI
10.1088/1751-8113/42/42/425203
Web versions
http://dx.doi.org/10.1088/1751-8113/42/42/425203
Language
English
Status of Item
Peer reviewed
ISSN
1751-8121 (Online)
This item is made available under a Creative Commons License
https://creativecommons.org/licenses/by-nc-sa/1.0/
Owning collection
Mathematics and Statistics Research Collection
Scopus© citations
11
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Feb 5, 2023
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Feb 6, 2023
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