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I'm trying to solve the restricted problem of three bodies, where a negligeable mass particule is moving in the gravitationnal field of two heavy objects which are in circular orbit around their common center of mass. this is a plane problem...

I describe the mouvment in the mobile referential in order to have an time independant hamiltonian, which is the following :

[tex]H = \frac{1}{2} ( P^2_1+P^2_2 ) + P_1Q_2-P_2Q_1 - (\frac{1-\mu}{R_1} + \frac{\mu}{R_2})[/tex]

where Q1,2 and P1,2 are the position and momenta of the object one and two respectively.

I found out that, since the energy is an invariant of this problem, there was a numerical algorithm which was better to use : symplectic method.

I don't know much about it, I just know it is better than classical RK4 (even with variable time step) because it preserves invariants and 'symplectic form' (I don't really know what it is...)

I'm french student in 2nd cycle physics studies, I learnt hamiltonian formalism this year, but not the "symplectic" notion... therefore, I don't really know how to code a symplectic integrator.

I didn't see a lot of web sites which could help me, just things like "Candy-Rozmus algorithm" which I don't really understand.

I found an exemple of a symplectic runge kutta function on the web

"http://aristote.obspm.fr/phynum/libphynum/lib1.html"

the code is here in this package : http://aristote.obspm.fr/phynum/libphynum/libphn.tar.gz

I'm looking for some help to understand this...

Thank you

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# Symplectic runge kutta for hamiltonian system

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