Corrigendum Re: Fwd: Evaluation of Hamilton equations by computer

OK thanks, the overall result is unaffected, p and q can be defined as gamma m v sub N and r in the Hamilton equations, where there is a freedom of choice of p and q. We know from the Lagrangian analysis that p = gamma m v sub N, the relativistic momentum of special relativity. Physics is changing very rapidly.

Corrigendum Re: [] Fwd: Evaluation of Hamilton equations by computer

Here comes the corrected graphics. The functions are not identical. There is essentially an additional factor of c^2/v^2 in the self-consistently determined gamma.

Horst

Am 03.01.2019 um 15:21 schrieb Horst Eckardt:

I had an error in the third graph of gamma-4.pdf. The curves for photons is not identical to that of Hamilton theory, but the asymptotic values are identical.

Horst

Am 03.01.2019 um 15:01 schrieb Horst Eckardt:

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-4.pdf


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