Periodic orbits of the 3-body problem

Last Christmas break, I tried to finalize some code for converging periodic orbits of the 3-body problem. I investigated the equal mass case. Candidates were identified from symplectic forward shooting and converged with Newton-lsqr. The whole code for converging 3D orbits is in C and it is blazing fast.

Some 2D solutions 

Some 3D solutions 

The C code for 3D solutions can be found here. I have spectral MATLAB code that computes these things globally and to machine precision. The MATLAB code can solve for the monodromy matrix and the Lyapunov exponents to machine precision with Newton-GMRES as well.

The end goal of this is to study Covariant Lyapunov Vectors (CLV) in this setting, since CLVs are exactly computable on periodic and relative periodic orbits.