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 {\em Annals
of Mathematics}  

Chenciner,~A., Gerver,~J., Montgomery,~R. and Sim\'o, C. [2000], Simple
Choreographic Motions of $N$ Bodies: A Preliminary Study, preprint.
Available at {\tt http://www.maia.ub.es/dsg}

Sim\'o,~C. [2000], New families of Solutions in $N$--Body Problems,
to appear in the {\em Proceedings of the ECM 2000}, Barcelona (July, 10--14).
Available at {\tt http://www.iec.es/3ecm}.

To see the animations please download the attached tar file. 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.

Put the tar file in some directory. Type (instructions appear as
<instruction> and names of files as "name")

<tar xf movie.tar>

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

Move to it:  <cd movie>

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 copy of this "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: <startmovie> 

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 graphycal devices.

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

<restart>

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: 

<gunzip nnnef.gnu.gz>

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

gnuplot>

please enter the following 

<load 'indiv/show1.xx.gnu'>

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 Sim\'o
