Some comments:
> -to start, a proper simulation of many gravitating bodies
> requires a
> clever integrator. You have to write a Runga-Kutta scheme
> that uses
> adaptive step-size control
I wrote one of those myself some years ago. The standard
solution is the Runge-Kutta-Fehlberg 4th/5th-order variable
timestep integrator ("RKF45"). You should be able to find
Fortran code for it online somewhere, and it's not too
difficult to understand Fortran. Or the Numerical Recipes in
C book has a number of ready-made solutions. If all else
fails, come back here and ask.
My integrator was somewhat special in that it needed to be
able to handle discontinuities, which don't occur in the
solar system -- assuming no collisions! (Discontinuities are
problematical because if you integrate across them, the
truncation error is theoretically unbounded.)
> There's a nice simplified model you could simulate to
> estimate
> the Lyapunov exponents.
One of my PhD students did something on this. Again,
discontinuous systems cause major problems, but that doesn't
apply here. Essentially the largest Lyapunov exponent is the
rate at which, on average, neighbouring trajectories diverge
exponentially from each other in a chaotic system.
> I can pay 100$ as a gift for person who does that.
No thanks, I don't need the money. But if I did, it would
cost a lot more than $100. :-)
David
