Re: [Phys-l] A numerical simulation of orbiting

[John Denker <jsd@av8n.com>]

On 12/30/2007 08:14 AM, Ludwik Kowalski wrote:
> .... Keep 
> in mind that I am asking this questtion in the context of a specific 
> problem. Three identical stars are initially at rest on the diameter of 
> a circle (2*R) .....

This problem is neither stable nor unstable.
This problem is neither chaotic nor non-chaotic.
This problem merely "is".  The solution is unique.  It just "is".
Stability has to do with /perturbations/ but this problem
as stated doesn't allow any perturbations.
Chaos has to do with sensitivity to initial conditions
(plural) but this problem as stated has only one initial
condition.

> 3) What is wrong with saying that an orbiting system, described above, 
> is stable when it is energetically bound? 

The problem is so narrowly specified that stability
questions cannot be asked, let alone answered.

> 4) Why am I insisting on limiting the discussion to a specific 
> three-body system? Because the circular orbit system is mathematically 
> simple. 

It's too simple.

> The fact that a moving system can possibly be unstable (or chaotic) 
> does not mean that it actually is unstable or chaotic. 

True.

> How to 
> distinguish a set of initial conditions that produces a stable moving 
> system from a set of conditions that produces an unstable system? 

In general, map the parameter space.

For example:
  http://en.wikipedia.org/wiki/Julia_set