+44 (0)1509 263171
Please use this identifier to cite or link to this item:
|Title: ||A theoretical analysis of billiard ball dynamics under cushion impacts|
|Authors: ||Mathavan, Senthan|
Jackson, Michael R.
Parkin, Robert M.
|Keywords: ||Impulse with friction|
Coefficient of restitution
|Issue Date: ||2010|
|Publisher: ||Sage Publications / © The Authors|
|Citation: ||MATHAVAN, S., JACKSON, M.R. and PARKIN, R.M., 2010. A theoretical analysis of billiard ball dynamics under cushion impacts. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 224 (9), pp. 1863 - 1873.|
|Abstract: ||The last two decades have seen a growing interest in research related to billiards.
There have been a number of projects aimed at developing training systems, robots, and computer
simulations for billiards. Determination of billiard ball trajectories is important for all of
these systems. The ball’s collision with a cushion is often encountered in billiards and it drastically
changes the ball trajectory, especially when the ball has spin. This work predicts ball bounce
angles and bounce speeds for the ball’s collision with a cushion, under the assumption of insignificant
cushion deformation. Differential equations are derived for the ball dynamics during the
impact and these equations are solved numerically. The numerical solutions together with previous
experimental work by the authors predict that for the ball–cushion collision, the values of
the coefficient of restitution and the sliding coefficient of friction are 0.98 and 0.14, respectively.
A comparison of the numerical and experimental results indicates that the limiting normal velocity
under which the rigid cushion assumption is valid is 2.5 m/s. A number of plots that show
the rebound characteristics for given ball velocity–spin conditions are also provided. The plots
quantify various phenomena that have hitherto only been described in the billiards literature.|
|Description: ||This article was published in the journal, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science [Sage Publications on behalf of IMechE / © The Authors]. The definitive version is available at: http://dx.doi.org/10.1243/09544062JMES1964|
|Version: ||Submitted for publication|
|Publisher Link: ||http://dx.doi.org/10.1243/09544062JMES1964|
|Appears in Collections:||Published Articles (Mechanical, Electrical and Manufacturing Engineering)|
Files associated with this item:
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.