for the periodic solutions
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
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).
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).
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.
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