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The impact characteristics of a cue in billiards are investigated for the case where a ball is hit on the right or the left part to give a spin. The efficient computational method developed in the previous paper is extended for this investigation. The extended method is verified with an experiment using a high speed camera, i,e., the ball trajectory calculated with the extended method is shown to agree well with that measured using a high speed camera. It is shown from a numerical simulation that the impact force, the ball velocity, the spinning velocity and the deviation of the ball trajectory from the hitting direction increase with increase in the Young's modulus and density of a shaft. Because the proposed analytical method can predict quantitatively these impact characteristics of a cue, it is useful for designing an easy-to-use cue.

Numerical Evaluation of Impact Characteristics of Cue in Billiards (Case Where Spin is Given on Ball)