Dynamics in carom and three cushion billiards

Abstract

This paper presents the analysis results of dynamics in the billiards game within the framework of rigid-body mechanics and a numerical simulation program. The friction exists between the ball and the table bed as well as between the ball and the rail. There are three parts in the dynamic behavior of the ball on the table bed, motion of the ball on the table bed, collision between balls, and collision between the ball and the cushion. During the development of the simulation program. the dynamics problems such as rolling motion and three dimensional frictional impact motion have been analyzed in detail. The theoretical issues are implemented into a viable graphic simulation program and its efficacy is demonstrated through the experimental validation of the billiards game. The resulting analysis results are verified quantitatively and qualitatively using high-speed video camera. Through the experimental tests. it was found that the physical parameters such as coefficients of restitution and friction vary according to the motion variables and corresponding empirical formulations were developed. The simulation and experimental results agree well.