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Perfectly centered break of a perfectly aligned pool ball rack

mathoverflow.net

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Re: Perfectly centered break of a perfectly aligned pool ball rack

#21

Post by tel »

waqf wrote: post #19
rcthompson wrote: post #12

Can anyone explain the "rules" for a 3-way simultaneous colision? Freshman physics only covered collisions between 2 objects, and I've never figured out how to generalize it.

Right, with 3 balls you can't just do an impulse calculation like you can with 2 (too many unknowns, too few equations). The author is simulating the collision as an event which happens gradually over an (admittedly short) period of time, using a differential equation, instead of something that happens all at once. That's why he has to talk about the elasticity model he's using, F ∝ (2-d)^1.5, and how the results var…

Could you get more equations by symmetry?

Re: Perfectly centered break of a perfectly aligned pool ball rack

#22

Post by IgorPartola »

joosters wrote: post #11
TheLoneWolfling wrote: post #10

This doesn't take into account rotation though :( See http://archive.ncsa.illinois.edu/Classes/MATH198/townsend/in... for including rotation.

Also doesn't take into account the direction of the nap of the cloth on the table - balls rolling 'up' will travel differently from those rolling 'down'. Would this also mean that the speed of the balls has to be taken into account? The differing effects of friction on the surface would surely alter as the balls move & spin slower?

Yes. Friction being constant is a lie that we tell middle school students. In undergrad physics you learn that there is also a linear and quadratic component. That is also a lie since even that assumes perfect balls, etc.

Re: Perfectly centered break of a perfectly aligned pool ball rack

#23

Post by taliesinb »

Really cool problem! And great animations.

I was disappointed to find that the associated notebook (http://math.bard.edu/belk/code/BilliardsHertz.nb) doesn't work correctly in either Mathematica 9 or 10 -- I think the author used 8.

It seems like NDSolve falls down:

NDSolve::smpf: Failure to project onto the discontinuity surface when computing Filippov continuation at time 0.`. >>

and the solution shows the cue bool passing through all the others..

Re: Perfectly centered break of a perfectly aligned pool ball rack

#24

Post by IgorPartola »

Somewhat meta, but at what point does Stack Overflow transition from being a useful, time-saving tool and become a waste of everyone's time? The top answer author clearly put a ton of time on the answer. We are all now reading this. Is anyone able to apply any of the knowledge they gained from this Q&A to anything productive?

Re: Perfectly centered break of a perfectly aligned pool ball rack

#25

Post by sillysaurus2 »

taliesinb wrote: post #23

Really cool problem! And great animations. I was disappointed to find that the associated notebook ( http://math.bard.edu/belk/code/BilliardsHertz.nb ) doesn't work correctly in either Mathematica 9 or 10 -- I think the author used 8. It seems like NDSolve falls down: NDSolve::smpf: Failure to project onto the discontinuity surface when computing Filippov continuation at time 0.`. >> and the solution shows the cue bo…

There's a Mathematica 10 now, already? Interesting.

I'm still a happy 8 user, myself. Is there much reason to upgrade?

It'd probably be good for them to pay more attention to backwards compatibility...

Re: Perfectly centered break of a perfectly aligned pool ball rack

#26

Post by matthewi »

taliesinb wrote: post #23

Really cool problem! And great animations. I was disappointed to find that the associated notebook ( http://math.bard.edu/belk/code/BilliardsHertz.nb ) doesn't work correctly in either Mathematica 9 or 10 -- I think the author used 8. It seems like NDSolve falls down: NDSolve::smpf: Failure to project onto the discontinuity surface when computing Filippov continuation at time 0.`. >> and the solution shows the cue bo…

That is odd. Mathematica is usually good about backwards compatibility. That sounds like a change in the under lying numerical solver.

Re: Perfectly centered break of a perfectly aligned pool ball rack

#27

Post by nardi »

IgorPartola wrote: post #24

Somewhat meta, but at what point does Stack Overflow transition from being a useful, time-saving tool and become a waste of everyone's time? The top answer author clearly put a ton of time on the answer. We are all now reading this. Is anyone able to apply any of the knowledge they gained from this Q&A to anything productive?

You need to stop and smell the billiard-ball-shaped roses, my friend. Not every pursuit needs be in the name of industry. Some people enjoy mathematical puzzles for their own sake.

Re: Perfectly centered break of a perfectly aligned pool ball rack

#28

Post by waqf »

tel wrote: post #21
waqf wrote: post #19

Earlier quoted context omitted.

Right, with 3 balls you can't just do an impulse calculation like you can with 2 (too many unknowns, too few equations). The author is simulating the collision as an event which happens gradually over an (admittedly short) period of time, using a differential equation, instead of something that happens all at once. That's why he has to talk about the elasticity model he's using, F ∝ (2-d)^1.5, and how the results var…

Could you get more equations by symmetry?

Yes … in the symmetric case. That might give you enough to solve the first one-against-two collision. But the subsequent collisions in the pool break problem won't be symmetric (the velocity of the "incoming" ball is not perpendicular to the axis joining the centers of the other two).

Re: Perfectly centered break of a perfectly aligned pool ball rack

#29

Post by dredmorbius »

IgorPartola wrote: post #24

Somewhat meta, but at what point does Stack Overflow transition from being a useful, time-saving tool and become a waste of everyone's time? The top answer author clearly put a ton of time on the answer. We are all now reading this. Is anyone able to apply any of the knowledge they gained from this Q&A to anything productive?

For those whose day job is modelling pool breaks, this could be a time-saving tool.

Actually, for anyone whose work involves modeling physics and collisions in general.

The fact that it describes a phenomenon with which a great many people are familiar and at least casually interested is only one aspect of this. And there's a long history of useful discoveries and advances coming from gaming and gambling (going back to Blaise Pascal).

Re: Perfectly centered break of a perfectly aligned pool ball rack

#30

Post by srean »

IgorPartola wrote: post #24

Somewhat meta, but at what point does Stack Overflow transition from being a useful, time-saving tool and become a waste of everyone's time? The top answer author clearly put a ton of time on the answer. We are all now reading this. Is anyone able to apply any of the knowledge they gained from this Q&A to anything productive?

I presume you know the story of Feynman and spinning plates [1]. Sense of play is important for productivity, sometimes it is more than just important, it becomes a necessity

[1] http://www.physics.ohio-state.edu/~kilcup/262/feynman.html

    The diagrams and the whole business that I got the Nobel
    Prize for came from that piddling around with the wobbling
    plate. -- Richard Feynman
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