425(1): Self Consistent results from the Lagrangian and Hamiltonian Methods
This note shows that the two methods are self consistent and produce a new equation (24) which is the generalization of the well known Eq. (25) of flat spacetime. For rigorous self consistency it follows that dm(r1) / dt = 0 and dm(r1) / dv1 = 0. This is because the fundamental infinitesimal line element and metric are those of a steady state universe. There is no expanding universe and no Big Bang. This was for example in UFT49. As shown UFT424, the fundamental equation (13) of Euler / Lagrange / Hamilton dynamics is true if and only of dm(r1) / dt = 0. All the results using the lagrangian theory of previous papers are rigorously correct: forward and retrograde precession, shrinking and expanding orbits, the possibility of superluminal motion, the possibilty of infinite energy from m theory, the description of the S1 star and the whirlpool galaxy, and in effect a completely new classical dynamics which overthrows the standard model on the classical level. Eq. (13) of fundamental Euler / Lagrange / Hamilton dynamics is obeyed rigorously by m theory, and the second Evans Eckardt equation dL / dt is given directly by both the classical method and the lagrangian method. The use of dH / dt = 0 and dL / dt = 0 gives Eq. (24), which gives new information on m(r1) and dm(r1) / dr1. The hamiltonian is given rigorously by the fundamental geodesic method, a Lagrangian method.