Re: [Phys-l] Simulating a disturbance of a stable planetary system.

[John Mallinckrodt <ajm@csupomona.edu>]

Because every instant of time is exactly the same as the initial  
instant of time in terms of the dynamics of this system.  There is no  
need to go to any lengths to apply a perturbation "at some later  
time" or "periodically" or "for a while" or anything else.  Simply  
change any ONE of the 12 initial conditions (i.e., the 2-d position  
and velocity components of the three particles) by a miniscule  
amount, push the start button, and watch the ensuing chaos!

John Mallinckrodt
Cal Poly Pomona

On Dec 31, 2007, at 9:39 AM, LaMontagne, Bob wrote:

> Ludwik,
>
> You seem to be repeating the same thing over and over expecting  
> hoping to get different results.
>
> Personally, I don't trust Interactive Physics - I prefer to program  
> a problem in Fortran or C. However, try using the random number  
> generator in I.P. to produce a series of small disturbances at  
> random times and random directions. A single disturbance has to  
> change the orbit. Real orbits are subject to both random and  
> periodic disturbances.
>
> Bob at PC
>
> ________________________________
>
> From: phys-l-bounces@carnot.physics.buffalo.edu on behalf of Ludwik  
> Kowalski
> Sent: Sun 12/30/2007 9:45 PM
> To: Forum for Physics Educators
> Subject: [Phys-l] Simulating a disturbance of a stable planetary  
> system.
>
>
>
> On Dec 30, 2007, at 7:16 PM, John Mallinckrodt wrote:
>
> > . . . An IP simulation will easily demonstrate this fact in a
> > minute or two and it will not be a computational artifact. . . .
>
> That issue emerged from my failure to demonstrate stability of a  
> simple
> two body system (a single planet revolving the sun along a circular
> trajectory). We expect such system to be stable (persistent). Using  
> the
> I.P. (Interactive Physics) I simulated the system and a short
> disturbance. Someone wrote that stability means ability to recover
> after a disturbance. In my simulation the new orbit (after the
> disturbance) was significantly different from the orbit before the
> disturbance. The period of revolution of the new (elliptical) orbit
> turned out to be longer that period of revolution of the initial
> (circular) orbit. In other words, the disturbance I applied was not
> self-correcting.
>
> The idea was to show that a disturbance applied to a two-body  
> system is
> self-correcting while the same disturbance applied to the three-body
> system is not self-correcting. How to implement an I.P. disturbance
> whose consequences disappear after the disturbance is over? I changed
> the subject line of the thread because this question has nearly  
> nothing
> to do with what has been discussed earlier today.
> P.S. To trust results of an experiment one often tests instruments by
> performing control experiments. The two-body simulation was to be a
> control experiment before the three-body simulation. But I was stuck,
> as described in a message posted two days ago.
> ________________________________
> 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/
> _______________________________________________
> Forum for Physics Educators
> Phys-l@carnot.physics.buffalo.edu
> https://carnot.physics.buffalo.edu/mailman/listinfo/phys-l
>
>
> <mime-attachment.txt>

A. JOHN MALLINCKRODT
Professor of Physics, Cal Poly Pomona
     http://www.csupomona.edu/~ajm
Acting Editor, AMERICAN JOURNAL of PHYSICS
     http://www.kzoo.edu/ajp

Professional/Personal email: ajm@csupomona.edu
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Phone: 909-869-4054
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