Orbit of figure eight 3 or more bodies

AI Thread Summary
To set up initial conditions for a three-body figure-eight orbit, specific position and velocity vectors must be defined for each body, along with their respective masses. The governing equations involve the force equations f=mi*x'' and f=SUM(mi*mj*r/|r|^2), which lead to a differential equation for the system. The discussion references additional resources for further understanding and examples of similar orbital simulations. The links provided lead to a website with detailed information on orbits and previous discussions on the topic. Understanding these principles is crucial for accurately modeling the dynamics of a three-body system in a figure-eight formation.
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
 
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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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