Continuing with UFT416

I need to work some more on the self consistency of the theory and to introduce new methods based ion the hamiltonian and geodesic equation. As described on the web the geodesic equation is a way of finding constants of motion. It is also described by Carroll , chapter seven of his online notes. Horst has shown in UFT415 that the lagrangian rigorously conserves total energy and angular momentum, but this lagrangian does not give p self consistently. This is why I weighted it as in Eq. (57) of UFT415. The lagrangian L is defined in hamiltonian / lagrangian dynamics by p = partial L / partial r dot, so that p = gamma m v / m(r) power half correctly. So it must be checked numerically whether the lagrangian of Eq. (57) of UFT415 gives a constant total energy and momentum. The lagrangian method must give p and L self consistently, such that the angular momentum L1 = r x p self consistently, and so that dH / dt = 0, dL1 / dt = 0.


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