Hey folks I'm looking into halo orbits and I have a question about how to find the initial conditions from the third order approximation solution... A good run through of the third order solution calculation is found in this paper. http://www.scribd.com/doc/36160757/ThurmanWorfolkGeometryHaloOrbits The Lindstedt-Poincare part begins on page 15. My questions are... The final approximation includes the [itex]\tau_1[/itex], [itex]A_x[/itex] and [itex]A_z[/itex] terms. These all contain the small parameter [itex]\epsilon[/itex] which hasn't been given a numerical value so how do I compute [itex]\tau_1[/itex], [itex]A_x[/itex] and [itex]A_z[/itex]?