414(5): Triple Cross Check Using the Hamiltonian Method.

This note shows that the hamiltonian method, dH / dt = 0, gives the same force equation as the kinematic and Lagrangian methods, thus giving a rigorous triple cross check on all calculations. All calculations are rigorously correct. There are hundreds of such cross checks in ECE and ECE2 theory. A quadruple cross check can be made using computer algebra. The lagrangian and kinematic methods have the advantage of being able to produce the relativistic angular momentum, and the lagrangian method shows that this is a constant of relativistic motion.So the lagrangian method is the most powerful method. It is more powerful than the Newtonian and kinematic methods as is well known. The quadruple cross check also shows that the correct Lagrange variables have been identified and used. So all available methods have been used. The orbit is given by simultaneous numerical solution of the relativistic force equation and the equation dL / dt = 0, where L is the relativistic angular momentum. This method can be used for any orbit in the universe, and can also be used to find the orbitals of the Sommerfeld atom in the old quantum theory, as would be expected of a unified field theory “of everything”.


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