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

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.