Evaluation of Hamilton equations by computer

This is indeed an important result, and congratulations! Effectively it gives a rigorous theoretical explanation for light deflection by gravitation using the Hamilton equations in special relativity, and a theoretical justification for the explanation of light deflection by gravitation in previous UFT papers. As you know, it was shown in UFT150 – UFT155 that the Einsteinian explanation is riddled with errors and obscurities, and is effectively pseudoscience. UFT150 – UFT155 are now classics, and cannot be covered up. This work of yours is spectacular proof that the Hamilton equations give important information in special relativity. Solving for gamma is a key idea, so it becomes possible to choose p = gamma m v sub N as a generalized coordinate, and q = r. You have also shown that the first order Hamilton equations can be integrated directly by the Maxima routine, another major advantage. The Hamilton equations of 1833 were first discovered by Lagrange in 1809, but attributed to Hamilton because he derived them using his Principle of Least Action.

Evaluation of Hamilton equations by computer

The Hamilton equations can be evaluted by computer. The equations can directly be given as input since they are of first order as the Runge-Kutta solver requires.
I have investigated the definition of the generalized gamma which – formulated with rel. p – is a function gamma=f(gamma,v). It is possible to resolve this equation for gamma, giving two solutions which are graphed in the protocol gamma.pdf. The second solution seems to be unphysical, the first has a pole at v=c/2. This gave me the idea to compare it to the gamma of photons which we derived as

gamma_ph =

.

The results are similar with a streching of the v axis. Therefore I introduced a factor in the definition of gamma as worked out in the second protocol gamma-4.pdf:

.
This gives two solutions again, and the second is identical to that for photons! We have gamma(v=c) = sqrt(2). I find this a remarkable result, bringing together different paths of our development.

Horst

Am 03.01.2019 um 10:28 schrieb Myron Evans:

Evaluation of Hamilton equations by computer

This is an excellent computer analysis of the Hamilton equations. In order to test the various results they can be compared with the orbits from the Lagrange equations and EE equations in the previous UFT papers. The Hamilton equations must give the same orbits as the Lagrange equations and Evans Eckardt equations. The EE equations are the most fundamental and powerful to date because of the ability of Maxima to integrate them. Can the Hamilton equations be integrated numerically? The lagrangian (L) can be computed from the fundamental L = p q dot – H for each choice of p and q in the protocol. This should lead to the lagrangian for special relativity used in previous papers. These results can also be compared with the Evans Eckardt equations for special relativity: dH / dt = 0 and dL / dt = 0, where H = gamma m c squared – mMG / r and L = gamma m r squared phi dot. In order to reduce correctly to classical theory only one choice of lagrangian and only one choice of hamiltonian is possible.

gamma.pdf
gamma-4.pdf


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