Finding gravitational n-body choreographies

Very interesting and a topic I have been very interested in (see e.g. N-Body on iOS or nbodyphysics.com).

Is there some minimal stability criteria for a curve to considered a choreography or is it enough that the path is an extrema of the action? Will e.g. the bodies make even one traversal of the path before going "off into the wild"?

I'd love a feature to extract positions and velocities for further study.

Awesome site.

The 3-body problem never ceases to amaze me. I've had so much fun playing with choreographies over the last few years, and detecting chaos. Despite the N-body problem being age-old, there's still so much cutting edge work being done on figuring out where various patterns and (sub)structures come from. The Kepler dataset [1] has provided a brilliant starting point to probe a lot of seemingly insane planet configurations.

One of the most fascinating restricted problems I've worked on is the Sitnikov problem [2].

[1] http://exoplanetarchive.ipac.caltech.edu/docs/KeplerMission....

[2] http://www.scholarpedia.org/article/Sitnikov_problem

It'd be interesting (but difficult) that the program can recognize the known choreographies (and rotated versions) and show the data.

It' difficult to find a choreography that is not a circle. I found the circle-with-hearth choreography and I was very happy until I saw (3-planets, position (6,1)).

And another feature request. I'd like to link to a choreography, at least to a well known choreography and perhaps to a user generated choreography.

Cris Moore and coworkers found a bunch of these http://tuvalu.santafe.edu/~moore/gallery.html Including this awesome 28-mass one http://tuvalu.santafe.edu/~moore/cubic28.loop.gif

Very cool! I can't wait until we become a type III civilisation and have animated constellations to look up at.

It would be interesting to know how fast they need to move and close you would need to place them to your home planet for the animation to be fast enough so you can observe a full loop in a couple of minutes.

It seems to me these choreographies are of theoretical interest, but in practice it would be hard to get a real choreography like those between planets

(Especially because of mass differences and the exact speeds they need to form those)

Which doesn't mean they might not form a different choreography

This is fabulous! I had heard there were figure-8 stable 3-body configurations but had never modeled one. Just sketch a figure-8 as the starting orbit and you'll see immediately how it works. Really beautiful work!

Would the symmetry groups (point groups?) be different for 3D?

Fantastic, but dangerous for your productivity ;)