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Re: [Phys-l] Interactive Physics Simulations

At 11:29 -0400 10/10/06, John Denker wrote:

On 10/09/2006 11:48 AM, Hugh Haskell wrote:

Making perfectly inelastic collisions has always been a problem for
IP. If have talked to them about it and they always tell me that it
is a difficult programming problem and they continue to work on it.

That's funny.

This is a physics problem, not a software problem.

From a purely software point of view, programming a macroscopic
description of an ineleastic collision is trivial. Consider the
case of two hard spheres colliding: Just conserve momentum
(including angular momentum) and ignore the energy equation,
i.e. thermalize however much energy you need to, in order to
make the momentum come out right. That's all there is to it.

The only way this gets to be hard is if you try to give a
microscopic accounting for the physics, in particular for the
thermalization step.

Moving to physics now, it is AFAIK impossible to have an
instantaneous inelastic collision. It's like trying to make
thin black paint: basically impossible. This is also related
to trying to "instantaneously" make the coupling between two
rail cars. Real-world rail cars don't even try to do it
instantaneously; they have "draft gears", as we discussed
back in November 1999 and on various occasions since.

So ..... you should plan on spreading the inelastic interaction
over some nonzero time and space. In this case I suggest making
an L-shaped (or upside-down T-shaped) pendulum and arranging for
the foot to stab into a nonzero-sized chunk of putty. It will
slow down bit by bit as it stabs deeper and deeper into the
putty.

I don't have any particular disagreement with what you say, all I was saying was that IP didn't manage to solve that problem very well. I think that it was for two reasons. First, their objects were always rigid ones, so their calculations of collision dynamics were never able to make the two objects that were supposed to be "stuck together" have exactly the same velocity, so they would stay stuck together. As Cindy pointed out, and I suspected might be possible, it can be done by putting in a suitably acting electric attraction between the two objects.

Of course, modeling a "real" inelastic collision is not simple, since it necessarily involved distortion of the colliding objects and a certain amount of microscopic intermingling to keep them together, and the collision time is relatively longer than with an inelastic collision. But IP treated inelastic colisions in a fairly simple-minded way, and I know that if I didn't do something "unphysical" in constructing the collision, the two objects would gradually drift apart, and this was especially true if one of the objects was rotating.

You also had to be careful not to make the time interval in the differential equation integration routine to large or the two object might pass through each other before they had time to interact, or more likely, one would penetrate an obseervable distance into the other before the interaction began.

While IP was a very useful instructional tool (at least before they decided not to support OS X), in order to do all the things it did, there were some corners cut that created problems if you tried to get too sophisticated. You could get pretty accurate solutions if you used the more sophisticated integration routines and short time intervals, but then the simulation ran so slow that it lost its instructional value, and if you made the time interval too long, then you ran into the type of problems I described above. You could record a slow simulation in a QuickTime movie, but then you couldn't make any changes to the problem parameters, to show alternative situations, which, to my mind was always one of the strong points of IP.

I haven't made much use of Wolfgang Christian's Physlets, so I really can't say whether they are a good alternative to IP or not. I suspect that they might be, for at least some types of problems.

Hugh
--

************************************************************
Hugh Haskell
<mailto:haskell@ncssm.edu>
<mailto:hhaskell@mindspring.com>

(919) 467-7610

When you are arguing with a stupid person, it is a good idea to make sure that
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