A new solution to the three body problem - and more

by Bill Casselman

4. More of Simó's choreographies

These have been selected more or less randomly from a collection of 47 choreography animations designed by Carles Simó to run in gnuplot, which have in turn been selected from several hundred possibilities he has examined. The data to make these plots have just been lifted from Simó's programs, in fact. The full collection of 47 animations can be obtained from http://www.maia.ub.es/dsg/nbody.html. Note that these choreographies are conjectural solutions to the problem of N equal point masses moving in the plane under their mutual gravitational attraction, the conjectures supported by computer analysis. Only the 3-body figure-eight has been proved to be an actual solution.

Click on an image to see an animation applet. The numbering is taken from Simó's sequence.

  • Four bodies
  • Five bodies
  • Six bodies in a non-symmetric choreography
  • Eleven bodies

Website of the AMS Comments:webmaster@ams.org
) Copyright 2001, American Mathematical Society