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A disc rolling in a tray

Published online by Cambridge University Press:  01 August 2016

Alan F. Beardon
Alan F. Beardon*
Affiliation:
Centre for Mathematical Studies, University of Cambridge, Wilberforce Road, Cambridge CB3 0WB
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Extract

Imagine a horizontal rectangular tray with vertical sides, and a disc lying flat in the tray and rolling around the inside of the tray in such a way that its circumference is always in contact with the edge of the tray. We shall suppose that the disc has been rolling for ever in the past, and that it will continue to roll for ever in the future. What can we say about this physical system? Our aim is to illustrate the complexity and the discontinuous nature of the system under arbitrarily small changes in the size of the tray (a feature that is typical of many dynamical systems).

Type
Articles
Information
The Mathematical Gazette , Volume 86 , Issue 506 , July 2002 , pp. 248 - 253
Copyright
Copyright © The Mathematical Association 2002

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References

1. Hardy, G.H. and Wright, E.M., An introduction to the theory of numbers, (5th edn), Clarendon Press (1979).Google Scholar