Three-body Problem: Lagrange Config, Equal Masses

[Stam]

I hope I'm on the right thread!
So i have the following problem...I have a homework on the three body problem. I want to simulate a 2D periodic circular problem using the Lagrange configuration. The masses of the three bodies are all equal to 1.
Can anyone tell me what initial conditions to use?

 

[pervect]

You'll basically have an equilateral triangle rotating about the center of mass. Calcluating the angular frequency, w, at which the rotation occurs is a bit tricky, though.

Do you expect this case with three equal masses to be stable?

 

[Stam]

I know that with equal masses it will be unstable...I know that in the bibliography there are some specific initial condititions for which a periodic orbit on a equilateral triangle will occur. I found the initial conditions (x1,y1,x2,y2,x3,y3,vx1,vy1,vx2,vy2,vx3,vy3) for the figure-8 orbit but i cannot found anywhere about the lagrange.

 

[tony873004]

http://orbitsimulator.com/BA/3-body.GIF
It is stable for a few orbits, then it falls apart.

Like Pervect said, its an equalateral triangle, so x,y,&z should be easy to find.

There's a wide range of velocities that will give you varying eccentricities.
sqrt(2GM/r) is what I used in the above picture. sqrt(3GM/r) gives you more circular orbits.

 

[Stam]

Or I'm too stupid or too tired ...Anyway I'm stuck. Can anyone give me a set of initial conditions because i have to hand in a homework tomorrow? Thanks for all the answers!

 

[enigma]

Sorry Stam,

We _help_ with homework, but we won't _do_ your homework here.

Assuming you're qualified to be in the class you're in, what tony and pervect provided is more than enough to get a solution.

 

[Stam]

Yes it's true. But my homework was to search the internet and find specific intial conditions and not to calculate them. My professor has given me a mathematica program to calculate three body orbits and all i have to do is search the internet, find exact numbers for the lagrange and figure-8 orbit, plot the orbit in mathematica and create a .gif with that orbit. I've found initial conditions for figure-8 but nothing for the lagrange orbit. Sorry for not mentioning that earlier!