Nice, I liked how I could see the relative attractiveness change as the bodies moved.
What was the shading on the bodies for? At first I thought the bright side might be pointed towards the centre of mass of the other two, but it seems not.
Nicely done - I like the option to spin around the group and get a 3D feel for it, but it seems that all the examples you have are strictly planar. Are there any true 3D solution to these choreographed N-body problems?
The problem is vastly easier with initial positions and velocities constrained to the plane. If they start that way, they can't ever leave. Even if you have a coulomb/newtonian potential, proving stability will be far more straightforward.
I'd love to be surprised, but I suspect closed and collisionless solutions with any out-of-plane components would be newsworthy and immediately publishable.
> closed and collisionless solutions with any out-of-plane components would be newsworthy and immediately publishable.
Trivial example: What about two tiny spaceships (they're small enough that their effect on each other is negligble) orbiting a star, one orbiting in the XY plane the other in the XZ plane?
Thanks. I'm not a physicist, I was merely drawing pretty pictures based on real physicists' work. The examples in the paper are all planar (and have zero angular momentum), but it would be easy to simulate arbitrary orbits if any are published.
I made some simulations of them using three.js: http://www.funcmain.com/three_body_problem
Mine are pretty much the same kind of examples as those posted here, except specifically for the case N=3.