Resources
for the periodic solutions

of plane 3 body problem

of plane 3 body problem

The 3- and n-body problem has been a challenge for analysis. In most cases of planar 3 body problem with equal masses and resting center of mass the trajectories look chaotic, or they end up in two bodies coupling and moving to infinity, while the third body moving also to infinity in the opposite direction.

Discoveries of periodic solutions of such 3-body problems was a challenge solved in the modern time with the help of computers. One of the scholars in this field is Ana Hudomal from the Institute of Physics at the Belgrade University. Thanks to her paper, all the initial conditions for 203 periodic solutions were entered into the Demo of the Taylor Center each of which can be loaded and played here. Here is how.

1) Go to Demo/3 bodies/Periodic (closed)/A list to
integrate (not a script)

2) Enter a number of the desired sample between 1 and 203 into a small window (top left). The program loads the ODEs for the 3 body problem with the initial values corresponding to the selected periodic orbit, compiles, and (blindly) integrates the problem until reaching the termination point – the period of this simulation entered from its file. (The period of the orbit is visible also in the Front panel in the*Constant* section
as a comment line for constant *a*).

3) When the integration reaches the termination point (the period), the program displays the message. As you click OK, the program opens the Graph window displaying the entire trajectory. You may wish to*Play* it
dynamically (by default the duration is 25 s). Depending on the
complexity of the curve, it may be
something like 60-80 seconds. Enjoy the show, and then repeat
everything from step 2 for another sample.

4) If you like the curves that you have obtained and played, you may wish to save this session as the script so that next time they integrate ready for playing automatically. In the File menu,*Save* Script into
a location of your choice (available only in the licensed version).
Next time you will be able to open this script and play it.

2) Enter a number of the desired sample between 1 and 203 into a small window (top left). The program loads the ODEs for the 3 body problem with the initial values corresponding to the selected periodic orbit, compiles, and (blindly) integrates the problem until reaching the termination point – the period of this simulation entered from its file. (The period of the orbit is visible also in the Front panel in the

3) When the integration reaches the termination point (the period), the program displays the message. As you click OK, the program opens the Graph window displaying the entire trajectory. You may wish to

4) If you like the curves that you have obtained and played, you may wish to save this session as the script so that next time they integrate ready for playing automatically. In the File menu,

Ana Hudomal: Initial Conditions of New Periodic Solutions of the Three-Body Problem, Institute of Physics, University of Belgrade, Pregrevica 118, Zemun, P.O.Box 57, 11080 Beograd, Serbia

http://three-body.ipb.ac.rs/sequences.php

https://doi.org/10.1088/1751-8121/aaca41