PS note 379(7)

Thanks again!

To: EMyrone@aol.com
Sent: 22/06/2017 16:31:37 GMT Daylight Time
Subj: Re: note 379(7)

Correction: (28,29) are correct.

Am 22.06.2017 um 17:05 schrieb Horst Eckardt:
> It seems that in eqs. (14,15) and (18,19) a dot is missing above X and
> Y at the LHS, stemming from bold v.
> At the RHS in (18,19) X dot dot has to be replaced by X resp. Y.
> in (28,29) the factor MG is missing.
>
> Horst
>

Checking note 379(7)

OK many thanks! Agreed, I fixed these typo’s in the final paper, UFT379.

To: EMyrone@aol.com
Sent: 22/06/2017 16:09:38 GMT Daylight Time
Subj: note 379(7)

It seems that in eqs. (14,15) and (18,19) a dot is missing above X and Y
at the LHS, stemming from bold v.
At the RHS in (18,19) X dot dot has to be replaced by X resp. Y.
in (28,29) the factor MG is missing.

Horst

379(7).pdf

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TCD and 21 Westland Row Dublin

Oscar Wilde was born at 21 Westland Row Dublin. Trinity College Dublin is partly based in some houses of Westland Row. My co author, Prof. William Coffey, had an office in one of them and showed me one of the elegant houses. Sir William Rowan Hamilton, my predecessor on the Civil List, was a student at TCD, a full professor at the age of 23. In Dublin he is known simply as Rowan Hamilton, a mathematical prodigy and a kindly man who would spend hours explaining a solution to anyone who wanted to learn. I am sometime Visiting Academic of Trinity College Dublin, part of the OxBridge system of Colleges. Rowan Hamilton was the discoverer of what are known as the Euler Lagrange equations, the Hamilton equations, Hamiltonian dynamics, the hamiltonian, quaternions, and much more. UFT175 and UFT176 infer the quantum Hamilton equations, both papers are by now classics.

Continuing with UFT380

There are many permutations and combinations possible of the field equations and I will carefully select the best way forward in the next note for UFT380. The numerical integration methods of the past few methods provide interesting solutions for each situation.

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380(2): Combined Gravitation and Electromagnetism, Biefeld Brown

This note gives a scheme of computation on page 7 by which the problem can be solved completely and in general. There are enough equations to find all the unknowns, given of course the skilful use of the computer by co author Horst Eckardt. The Biefeld Brown effect is explained straightforwardly by Eq. (14), which shows that an electric charge density can affect the gravitational scalar potential and therefore can affect g. I did a lit search on the Biefeld Brown effect, it has recently been studied by the U. S. Army Research Laboratory. This report can be found by googling Biefeld Brown effect”, site four. There are various configuration which can all be explained by Eq. (14) – asymmetric electrodes and so on. In the inverse r limit the total potential energy is given by Eq. (19). This gives the planar orbital equations on page 4 of the Note. These can be solved numerically to give some very interesting orbits using the methods of UFT378. The lagrangian in this limit is Eq. (29) and the hamiltonian is Eq. (30). These describe the orbit of a mass m and charge e1 around a mass M and charge e2. If Sommerfeld quantization is applied this method gives the Sommerfeld atom. Otherwise in the classical limit it desribes the orbit of one charge with mass around another. The equations are given in a plane but can easily be extended to three dimensions. Eqs. (31) to (34), solved simultaneously and numerically with Eqs. ((37) and (39), the antisymmetry conditions, are six equations in six unknowns for gravitation and six equations in six unknowns for electromagnetism. These equations give the spin connections and vector potentials in general (three Cartesian components each).

a380thpapernotes2.pdf