The dynamics of a bouncing superball with spin
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Aston, Philip J. and Shail, Ronald (2007) The dynamics of a bouncing superball with spin Dynamical Systems, 22 (3). pp. 291-322. ISSN 1468-9367
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Abstract
When a superball is thrown forwards but with backspin, it is observed to reverse both direction and spin for a few bounces before settling to bouncing motion in one direction. The bouncing ball is modelled by a two-dimensional iterated map in terms of the horizontal velocity and spin immediately after each bounce. The asymptotic motion of this system is easily determined. However, of more interest is the transient behaviour. The two-dimensional linear map is reduced to a one-dimensional nonlinear map and this map is used to determine the number of direction and spin reversals that can occur for given initial conditions. The model is then generalised to describe a ball bouncing up and down a single step or successively down a staircase.
| Item Type: | Article |
|---|---|
| Additional Information: | This is a pre-press version of an article published in Dynamical Systems, 22, 291-322. Click here to access the published version. © 2007 Taylor and Francis Group. |
| Uncontrolled Keywords: | Bouncing ball, spin, direction reversal, spin reversal, staircase. |
| Divisions: | Faculty of Engineering and Physical Sciences > Mathematics |
| ID Code: | 1537 |
| Deposited By: | Mr Adam Field |
| Deposited On: | 27 May 2010 15:42 |
| Last Modified: | 28 Sep 2012 10:50 |
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