The dynamics of a bouncing superball with spin
Aston, PJ and Shail, R (2007) The dynamics of a bouncing superball with spin DYNAMICAL SYSTEMS-AN INTERNATIONAL JOURNAL, 22 (3). 291 - 322. ISSN 1468-9367
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Official URL: http://dx.doi.org/10.1080/14689360701198142
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.
|Additional Information:||This is an electronic version of an article published in Dynamical Systems, 22 (3), 291-322 (2007). Dynamical Systems is available online at: http://www.tandfonline.com/action/doSearch?type=simple&filter=multiple&stemming=yes&searchText=The+dynamics+of+a+bouncing+superball+with+spin&publication=40000149&x=37&y=12http://www.tandfonline.com/action/doSearch?type=simple&filter=multiple&stemming=yes&searchText=The+dynamics+of+a+bouncing+superball+with+spin&publication=40000149&x=37&y=12|
|Uncontrolled Keywords:||Science & Technology, Physical Sciences, Technology, Mathematics, Applied, Mechanics, Mathematics, TIPPE TOP, RATTLEBACK, BALL, KINEMATICS|
|Divisions:||Faculty of Engineering and Physical Sciences > Mathematics|
|Deposited By:||Symplectic Elements|
|Deposited On:||21 Dec 2011 09:41|
|Last Modified:||16 Feb 2013 16:47|
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