This is beautiful.

Which version of mathematica are you using? I tried your notebook in M10.0.2 and it threw errors and the manipulate didn't work as your animated gif shows that it does.

$System is "Mac OS X x86 (64-bit)"

This comment on the reddit thread:

Assuming the two corner balls don't bounce back and interfere, it looks like this break would sink two of the balls in the side pockets on an 8 foot table: https://dl.dropboxusercontent.com/u/27794628/BilliardsHertz2.gif

links to the nice simulation below.

Cool, excellent work !

Suddenly, I come up with one interesting question for billiards. As Vitaliy shows the full range of billiard table, is that possible to calculate the possibility, that all balls fall into holes just by one-shot-break. Possible or not possible, for 15 balls, can it be proved or verified by mathematics.

I mean, it’s just from perfect physical and theoretical prospective. It will be very hard for human and need high precision, not for practice. I don't know, if any professional player has ever done before, or any recording for this very rare things.

Maybe, A further question, how many balls (those balls consist of an initial triangular billiard) can be done by one-shot-all-fall.

Anyway, I think the current model can be use to analisys bowling ball as well. Bowling game is simple than billiard, no bounce and no trajectory.

Why are there no attachments anymore? Jim, your Bard webpage also seems to have disappeared. Do you still have a copy of this notebook/Manipulate? I'd love to play with and add to it!

Your article is very informative. As a billiards player I wonder what the best technique to break the rack in order to sink a ball, thus remaining the shooter. I'm assuming your analysis does not include horizontal rotation (english) of the cue ball as it hit the head ball of the rack. Also, can you evaluate a break from the rail at the first diamond as many players shot from this position. Is it the best position to sink at least one ball (not the cue ball)?

The code is available again in the main post. Thanks to Dr. James Belk for providing it.