Welcome to the choreographies of the N-body problem!

These are periodic solutions of the classical planar N-body problem, all the bodies having the same mass, and such that they travel along the same path on the plane. The animations displayed here correspond to the Newtonian problem, the masses are equal to 1, the period is 2\pi and the gravitational constant is set equal to 1. Some references are:

• Chenciner, A. and Montgomery, R. [2000], A remarkable periodic solution of the three body problem in the case of equal masses, to appear in Annals of Mathematics
• Chenciner, A., Gerver, J., Montgomery, R. and Simó, C. [2000], Simple Choreographic Motions of N Bodies: A Preliminary Study, preprint. Available at http://www.maia.ub.es/dsg
• Simó, C. [2000], New families of Solutions in N-Body Problems, to appear in the Proceedings of the ECM 2000, Barcelona (July, 10-14). Available at http://www.iec.es/3ecm.

To see the animations please download the movie.tar file (click here to download). It requires a linux/unix operating system, despite it is possible to modify instructions so that it runs in other systems. It uses gnuplot version 3.5 (pre 3.6) or any more recent version. Remark : Please, make sure you have a recent version of gnuplot before complaining it gives some errors.

Put the tar file in some directory. Type

It creates a subdirectory named "movie" which contains all the required files.

Move to it:

It should contain two executable programs ("startmovie" and "restart"), 49 compressed file (containing either data or instructions; do not uncompress them, because they are used in compressed form), a text version of these instructions in the "README" file, a file with the names of all the choreographies shown ("indivlist") and a subdirectory ("indiv"). The use of this one is described later.

Just type:

and the animations start. They appear one after the other. After displaying a choreography, the program pauses. You are prompted to continue by pressing <return>.

The time to run the full set of animations depends strongly on the type of computer and on the graphical devices.

In case something is wrong or you stop execution before the end, please type

to return to the initial conditions.

If you want to see the animations individually (check the file "indivlist" to see the different ones), you should uncompress a file:

Then start to run gnuplot. When you are prompted to introduce instructions by

please enter the following

where xx denotes any two decimal digits number between 01 and 47.

After running in this individual mode, one should type restart, to clean or compress auxiliary files.

Good luck and enjoy them!

Carles Simó