The dynamics of a bouncing superball with spin
Aston, Philip J and Shail, R (2007) The dynamics of a bouncing superball with spin Dynamical Systems, 22 (3). pp. 291-322.
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 non-linear 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.
|Divisions :||Faculty of Engineering and Physical Sciences > Mathematics|
|Date :||30 July 2007|
|Identification Number :||https://doi.org/10.1080/14689360701198142|
|Additional Information :||This is the authors' preprint of an article published in its final version in Dynamical Systems 22, 291-322|
|Depositing User :||Mr Adam Field|
|Date Deposited :||27 May 2010 14:41|
|Last Modified :||23 Sep 2013 18:33|
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