Invisible <voi### [at] devnull> wrote:
> As an aside, I tried to implement this on my laptop at the weekend, but
> it was hopelessly unstable. Today it seems very stable indeed. I can
> only assume this is to do with replacing Euler with 4th-order
> Runge-Kutta. I'm surprised it makes quite this much of a difference
> though...

The stability region for linear problems is a bit larger*, not to mention the
fact that it's, well, fourth order.  Of course gravitation has ugly
singularities, so it usually just seems to be the case that it doesn't blow up
as badly as Euler near singularities.  You can always divide by (r+epsilon)^2,
just to smooth things out--as long as you don't care about accuracy.  There are
much more robust methods, though:

http://tableau.stanford.edu/~mwest/group/Variational_Integrators
http://tableau.stanford.edu/~mwest/full_text/LeMaOrWe2004.pdf

 - Ricky


* http://www.scholarpedia.org/article/Runge-Kutta_methods#Stability

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