Orbit of figure eight 3 or more bodies

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SUMMARY

To establish a three-body figure-eight orbit, one must define the initial position and velocity vectors for each body, as well as their respective masses. The governing equations include Newton's second law, expressed as f=mi*x'', and the gravitational force equation f=SUM(mi*mj*r/|r|^2). These equations can be combined to derive a differential equation that describes the motion of the bodies. For further reference, users can consult the provided links to detailed discussions and simulations on orbits.

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renegade05
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If I wanted to set up some initial conditions for a 3 body figure eight orbit, what would I have to set the position and velocity vectors?

Say I have three vector inputs:
initial position <x,y>
initial velocity <x,y>
mass of bodies <m1,m2,m3>

The solutions for position use
f=mi*x''
f=SUM(mi*mj*r/|r|^2)

and equating the two to get a differential equation.

Hope this make sense.

See this for a reference of what I am trying to do:
http://www.ams.org/samplings/feature-column/fcarc-orbits3
 
Astronomy news on Phys.org
We discussed this on my website. You can find some info here:
http://www.orbitsimulator.com/cgi-bin/yabb/YaBB.pl?num=1181200864/0
http://www.orbitsimulator.com/cgi-bin/yabb/YaBB.pl?num=1250625868/0#0
 

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