By Pomponio A.
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Extra resources for Coupled nonlinear Schrodinger systems with potentials
These are the only situations that result in Îelastic=0. e. one clockwise and the other counterclockwise), then Î elastic will be negative, and the departure angle will depend on the relative magnitudes of the two components Î elastic and Îinelastic. Note that cos(D) depends on the final spin/speed ratios of the balls, so within the current set of simplifying approximations, the contribution of Îelastic to the departure angle is independent of the overall shot speed. The above qualitative analysis did not require a detailed examination of the forces during the collision process.
2) For the particular shot of interest, estimate the distance D from the object ball to the pocket; the corresponding maximum throw distance will be µbbD. (3) For the zero-friction cut angle 45 for the particular shot of interest, estimate the impact parameter for the ball-ball collision, and the ratio bbb/R. (4) Multiply the maximum throw distance µbbD by the impact parameter ratio bbb/R, and call the result s. (5) Imagine a point that is displaced by the distance s from the pocket target, and aim for this offset point as if there were no throw.
7 (in general, it is an even function, symmetric about å=0). 15), decreases to the value of zero at ( max ) , and then approaches its asymptotic value of -5⁄7 as the cut angle approaches π/2. Another point of interest shown in Fig. 7 is the value of the cut angle å at which the slope value of one. 963 deg]. For cut angles d less than åcrit, d NR >1 and the natural roll cue ball trajectory is more sensitive than the object ball trajectory to small variations in the cut angle. However for the rest of the d range of cut angles, d NR <1 and the cue ball trajectory is less sensitive than the object ball trajectory.
Coupled nonlinear Schrodinger systems with potentials by Pomponio A.