Re: [Phys-l] Sharing a problem for students

[John Mallinckrodt <ajm@csupomona.edu>]

Ludwik,

It should be quite apparent that your system is highly unstable.  But  
because you have an IP simulation, it is completely trivial to do the  
experiment and to gain considerable insight about the dynamics in the  
process.  Have you really not done it yet?  (As a Mac user, I've been  
abandoned by IP and sorely miss being able to use it.)

Simply perturb the initial conditions of your system in some  
arbitrary and arbitrarily minute way: i.e. change any position or  
velocity component from the perfectly symmetric situation you  
describe to one that is ALMOST but not quite perfectly symmetric.   
Then let it run.  What you will see is that the negatively charged  
central body will approach one or the other of the positively charged  
bodies, reducing the net force on the OTHER positively charged body,  
whereupon it will "escape" leaving the other two drifting off, bound  
in a two body Kepler orbit.

John

On Dec 21, 2007, at 11:38 AM, Ludwik Kowalski wrote:

> On Dec 21, 2007, at 11:37 AM, Bob Sciamanda wrote:
>
> > If you do a search (Google, Wikipedia, etc) you will find "dynamic
> > equilibrium" usefully defined
> > only for chemical and biological interactions.  In Mechanics a
> > somewhat related set of  useful concepts is stable vs unstable
> > equilibrium.
> >
> > Note that in mechanics we say that an object at rest under the action
> > of a set of forces which sum to zero is in a state of static
> > equilibrium.  This same object could be said to be in a state of
> > dynamic equilibrium when viewed from a different frame, in which the
> > object is in motion.  This distinction does not add much and  
> > AFAICT is
> > not used.
>
> Thanks Bob,
> 1) I changed the verbal description slightly at
>
>   http://pages.csam.montclair.edu/~kowalski/cf/339students.html
>
> (see the ending of point 5).
>
> 2) Is there any reason to think that my electrical orbiting system
> (three equal masses) will be less durable that a binary star or a  
> solar
> system? Unfortunately, the Interactive Physics does not allow to
> simulate in 3 dimensions.
>
> 3) Is my virtual displacements argument, and Figure 2, sufficiently
> convincing that the initial plane of the orbit will not change (in our
> laboratory frame)?
>
> 4) Using the IP simulation, I did what I wanted to do yesterday, but
> did not know how. The suggested idea was to create a short time
> disturbance and to show that original trajectories of rotating
> particles are not restored after the disturbed parameter is restored.
> This should have been obvious but a simulation was worth creating. The
> disturbed parameter was the mass of one positive particle. It was
> changed from 1.0 kg to 1.1 kg  for the duration of 0.01 seconds.  What
> do you think happened? Close your eyes, produce the answer and then
> read the next paragraph.
>
> The particle whose mass was disturbed started moving away from the
> other two particles. These two particles started spiraling toward each
> other. They ended orbiting elliptically around each other (like a
> binary star, I suppose). The trajectory of the third particle was
> becoming a straight line. Naturally, I could have disturbed any other
> parameter, for example, the speed of one particle, the location of the
> negative particle, etc. The term "dynamic equilibrium" was not
> appropriate because it implied that the original trajectories would be
> restored (after restoring what was disturbed). The IP could be an
> effective teaching tool.
> _______________________________________________________
> Ludwik Kowalski, a retired physicist
> 5 Horizon Road, apt. 2702, Fort Lee, NJ, 07024, USA
> Also an amateur journalist at http://csam.montclair.edu/~kowalski/cf/
>
> _______________________________________________
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John Mallinckrodt
Acting Editor, American Journal of Physics
Professor of Physics, Cal Poly Pomona