Numerical simulations of the frictional collisions of solid balls on a rough surface

Three-dimensional simulations of the frictional collision between solid balls moving on a rough surface are analyzed in this paper. The analysis is performed in the context of pool and snooker, two popular games in the pocket billiards family. Accurate simulations of ball motion in billiard games ar...

Full description

Saved in:
Bibliographic Details
Published in:Sports engineering 2014-12, Vol.17 (4), p.227-237
Main Authors: Mathavan, S., Jackson, M. R., Parkin, R. M.
Format: Article
Language:English
Subjects:
Biomedical Engineering and Bioengineering
Collisions
Computer simulation
Differential equations
Dynamical systems
Dynamics
Engineering
Engineering Design
Games
Materials Science
Mathematical models
Original Article
Rehabilitation Medicine
Sports Medicine
Theoretical and Applied Mechanics
Three dimensional
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Three-dimensional simulations of the frictional collision between solid balls moving on a rough surface are analyzed in this paper. The analysis is performed in the context of pool and snooker, two popular games in the pocket billiards family. Accurate simulations of ball motion in billiard games are useful for television broadcasts, training systems and any robotic game playing systems. Studying solid ball collisions in a three-dimensional space requires careful consideration of the different phenomena involved in ball motion such as rolling, sliding and ball spin about a general axis. A set of differential equations are derived describing ball dynamics during collisions. In the absence of explicit analytical solutions to the differential equations, a numerical procedure is performed to determine post-collision ball velocities and spins after collision. In addition, the paper also presents a methodology to analyze the curved, slip trajectories of balls immediately after impact. The results presented here, when compared with some experimental shots, show that the percentile errors in post-collision velocities are reduced by the proposed method. The prediction accuracies for ball travel direction are increased twofold by the proposed impact simulation algorithm.
ISSN:1369-7072
1460-2687
DOI:10.1007/s12283-014-0158-y