Re: [Phys-l] Phys-l Digest, Vol 36, Issue 1

[Ludwik Kowalski <kowalskil@mail.montclair.edu>]

On Jan 1, 2008, at 2:10 PM, Alfredo Louro wrote:

> If you change the initial conditions, you must get a different
> stable orbit, I think. There is no reason why it should decay
> back to the original initial conditions before you perturbed
> it. It seems to me you are solving two different problems.

I agree. That is why I now think that defining stability in terms of 
"returning to the original state of motion" (state of motion before a 
small perturbation was applied) is not reasonable. In view of my 
experience with I.P. simulations, I now think that stability, in 
situations being discussed, should be defined in terms of the loss of 
periodicity. For a two-body system periodicity is not lost (a singular 
circular orbit is replaced by two coupled elliptical orbits), but in 
the case of the three-body system, periodicity is lost and motion 
becomes chaotic (after the same kind of perturbation). All this can be 
simulated in I.P.
P.S.
The first thing I did, in this year 2008, was to simulate a pencil 
standing vertically on its sharp point. We know that, in reality, this 
kind of equilibrium is unstable. But the pencil on my screen remained 
vertical. Why was it so? Because the I.P. code ignores minute 
disturbances which are always present. The pencil started falling when 
a tiny additional weight was places on a side of its flat upper 
surface. I love I.P.
_______________________________________________________
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/