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I'm trying to figure out what kind of initial conditions I should put in my program in order to have stable trajectories.

Just to remind, The restricted problem of three bodies suppose that you've got two heavy masses in circular orbit around their common center of mass, and a negligeable mass particule orbiting in that system.

well, now we know that lets go further. In the equations describing this system, you probably know that there is a constant called the jacobi's integral.

This constant is J = -2*K, where K his the http://nicolas.aunai.free.fr/cours/magistere/p3cr/cvn/toto.jpg [Broken])

you can see a little plot here : http://nicolas.aunai.free.fr/cours/magistere/p3cr/cvn/cvn.gif [Broken]

representing those areas.

Well, since I'm looking for some stable trajectories, I thought that I could find a family of {Q1,Q2,P1,P2} variables which satisfies the relation J=-2K.

the problem is that I don't know how to do this... since my hamiltonian isn't trivial

is someone here got a idea ?

thx for all

bye

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# Initial condition of the restricted problem of three bodies

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