triple_r wrote:
>> Finally, I'm not sure that your system is chaotic.  For inverse-square
>> springs it's known as Euler's three-body problem and appears to have a
>> (rather complicated) analytic solution.
> 
> I'm not sure that immediately disqualifies it.  That's an interesting question
> though.  Can a dynamical system with an analytical solution be chaotic?
> Certainly not without a series solution, but still.  It's easy enough to come
> up with aperiodic functions that solve a deterministic, dynamic system (sin(x)
> + sin(pi x), for one), but I can't think of any ODE's with an analytical and
> chaotic solution.

Yeah, I wasn't sure either.  On further investigation it looks like it 
probably doesn't.  I was able to find some references to chaotic 
difference equations which had analytic solutions.  I couldn't find 
anything about ODEs though (at least not without wading through some 
papers).

I'm now much more curious about whether or not the system is indeed 
chaotic.  If I get enough time to actually digest them, maybe I'll take 
a deeper look at the analytic solution and see if I can figure out 
what's going on there.

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