This is the Euler Lagrange theory of these orbits. From previous work in UFT328 for example they are known to produce precession. So the theoretical precession from this fundamental theory is matched with the experimental precessions of the perihelion. The Euler Lagrange method can also be used in quantization and relativistic quantization, for exaemple in the H atom, Sommerfeld, Schroedinger and Dirac theories. The Maxima code can solve essentially all these problems unless they get too complicated as in the description of orbits with Euler angles. Only a white haired raving maniac would attempt that by hand. The Euler Lagrange method can also be used to derive the ECE2 field equations of electrodynamics, gravitation, hydrodynamics and dynamics. The Hamilton Principle is the basis for much of physics, discovered by my Civil List predecessor Sir William Rowan Hamilton in the early nineteenth century. He was appointed full professor at Trinity College Dublin at the age of twenty three. He was never an F. R. S. because he could not afford the fees. The hamiltonian is the basis for all of quantum mechanics as is well known and the lagrangian is very similar to the hamiltonian in most problems, the sign of the potential energy being reversed. This is not always true however, an as usual, care must be taken. Horst Eckardt, Doug Lindstrom, others and I hammer out all technicalities in every UFT paper. These papers are now a central part of physics, having a huge and permanent worldwide readership in all the best universities.