Hah, my high school memories - a graphical gravity simulator project for my CS class, leaking energy due to the use of a very naive integrator (the Euler method for ODEs).
You might want to try Stormer-Cowell, it's sort of a gold standard in orbit simulation.
UPDATED: Hmm, now that I think of it, this would probably profit more from a variable step method. Some of the close approaches seem to be really close for a fixed-step integrator.
Heh, that's exactly what I made with a friend for a physics project in high school. We didn't even consider different methods--we used the Euler method because it's the most intuitive. I didn't even know it had a name!
This is very helpful, thanks! It's interesting to see how many 'near misses' there are in the new solutions (e.g. butterfly_1) -- a point that wasn't clear to me from the original plots.
awesome work! If you get all configurations to be stable (maybe decrease the dt in addition to RK?) you can thank the scientists by sending a link to your work, I'll bet they'll be very happy with such pretty renderings.
I find it surprising that some configurations are as stable as they are with the simple integration method. At least (if I'm reading this correctly) you calculate positions and velocities at different times.
You might want to try Stormer-Cowell, it's sort of a gold standard in orbit simulation.
UPDATED: Hmm, now that I think of it, this would probably profit more from a variable step method. Some of the close approaches seem to be really close for a fixed-step integrator.