Three body simulation in Mathematica

Dear Classmates,

Lately, I have been very interested in chaotic motions. To explore properties of chaotic motion, I have looked at chaotic pendulum and three particles under 1/r^2 forces.

If we include air-friction and some force then simple pendulum is not very simple. The motion is very chaotic and not predictable. 

Here are some phase-space diagrams:

Here I plotted amplitude vs. force (at normal frequencies)

Here is a zoomed in version

As we can see, even the most chaotic pendulum has patterns in some phase-space diagrams.

How is this relevant to Astrophysics?

The N-body simulations are also chaotic. I have started my research to find any patterns in  the behavior of 3-bodies under gravitational force. I do this by setting up the differential equations of motion in Mathematica and using random values as initial conditions. I try to plot different phase-spaces to see any kind of patterns. 

Here is one of the video that shows the motion of three-body over time.

For some reason this video doesn't work. Here is a link to youtube link to this video.

If you like to play around with numbers, I have included the Mathematica source code. 

Why spend time?

Astrophysicists wants to find out how a star forms, how it dies, and the complicated phases it goes through during its evolution. Many scientists have made simulations of these events, but they take months to render in world's fastest super computers. 

If we can find alternative way to calculate motion of N-bodies (alternative to newton's motion), then we can run this simulations at very low costs and more efficiently. This would also help us understand complicated star evolution processes.

3-body 2D Source code

2-body 2D Source code

Special thanks to Mathematica