n-body choreography

An n-body choreography is a periodic solution to the n-body problem in which all the bodies are equally spread out along a single orbit.[1] The term was originated in 2000 by Chenciner and Montgomery.[1][2][3] One such orbit is a circular orbit, with equal masses at the corners of an equilateral triangle; another is the figure-8 orbit, first discovered numerically in 1993 by Cristopher Moore[4] and subsequently proved to exist by Chenciner and Montgomery. Choreographies can be discovered using variational methods,[1] and more recently, topological approaches have been used to attempt a classification in the planar case[5]


  1. 1 2 3 Vanderbei, Robert J. (2004). "New Orbits for the n-Body Problem". Annals of the New York Academy of Sciences. 1017: 422–433. arXiv:astro-ph/0303153Freely accessible. Bibcode:2004NYASA1017..422V. doi:10.1196/annals.1311.024. PMID 15220160.
  2. Simó, C. [2000], New families of Solutions in N-Body Problems, Proceedings of the ECM 2000, Barcelona (July, 10-14).
  3. "A remarkable periodic solution of the three-body problem in the case of equal masses". The original article by Alain Chenciner and Richard Montgomery. Annals of Mathematics, 152 (2000), 881–901.
  4. "Braids in classical dynamics". Moore's numerical discovery of the figure-8 choreography using variational methods. Phys. Rev. Lett. 70, 3675.
  5. Montaldi, James; Steckles, Katrina. "Classification of symmetry groups for planar n-body choreographies". arXiv:1305.0470Freely accessible.

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