Right, agreed, this will be fixed in the final paper as usual. Our system of checking, graphics and computer algebra is also first class, and the entire theory is based on irrefutable Cartan geometry. Our papers have been refereed and checked hundreds of thousands of times by a vast and permanent readership coming from the best universities, institutes, corporations, military facilities and similar in the world. Our scientometrics are uniquely accurate and detailed.
To: EMyrone@aol.com
Sent: 27/06/2017 18:28:33 GMT Daylight Time
Subj: Re: Discussion of 380(4)When inserting eqs. (10,11) into (9), I obtain the equation
curl (- omega sub 0 Q) – partial / partial t (omega x Q) = 0
which gives a sign change when moving the second term to the RHS.
Horst
Am 27.06.2017 um 10:16 schrieb EMyrone:
I think that Eq. (13) is OK, because it is derived from
curl (- omega sub 0 Q) = – partial / partial t (omega x Q)
To: EMyrone
Sent: 26/06/2017 15:44:41 GMT Daylight Time
Subj: Re Re: Discussion of 380(4)Shouldn’t there be a minus sign in eq.(13)?
Horst
Am 26.06.2017 um 16:20 schrieb Horst Eckardt:
It seems that in eqs.(16-18) of the note the dime derivatives at the LHS are missing.
Horst
Am 26.06.2017 um 09:56 schrieb EMyrone:
Agreed entirely. Eqs. (16) to (23) make up the set of simultaneous spatial equations in three dimensions, and can be solved for the Q three vector and spin connection four vector in general, for any situation in gravitation and electrodynamics, and combination therefore. In electrodynamics they can be used to solve for the A three-vector and the spin connection four-vector in general. I gradually worked towards this new general solution in the four notes. This is equivalent to a general solution of the EEC2 field equations in three dimensions. So we can now address any problem in physics, chemistry and engineering. Guesswork is no longer needed for the spin connection. In this set of equations there are only space variables, and I think that the computer can deal with the problem of solving a set of seven, fairly simple, simultaneous partial differential equations in seven unknowns, the three scalar components of Q or A and the four components of the spin connection. The general solution can be simplified, and any coordinates can be used, not only the Cartesain. However the Cartesain is the clearest as you inferred some time ago. The Eckardt / Lindstrom methods can be added to this new method. The solutions will almost certainly produce some very interesting spatial graphics. Having found omega sub X and onega sub Y from this genreal method, one can go back to teh orbital equations to see qhat kind of orbits emeerge, and one can addres the Biefeld Brown effect in a self consistent way. Finally, Q or A is also time dependent: Q = Q (t, X, Y, Z); A = A(t, X, Y, Z). An example is plane waves. The scalar potential is also t and space dependent in general.
To: EMyrone
Sent: 25/06/2017 15:55:21 GMT Daylight Time
Subj: Re: 380(4): Compleet Solution in Three dimensions.It is not se easy to find a set of equations which can give well defined field solutions. For example there must be time and space derivatives for each variable to give unique solutions. The Lagrangian seems mainly to be used to obtain time trajectories of orbits but not for general field solutions. In so far I am not sure if it makes sense to use the LHS of eq.(3) for determining distributed fields Phi and bold omega.
Eqs.(16-23) is a more general scheme which seems to fulfill the above condition. For a solution, the boundary conditions are essential, because there are no terms of inhomogeneity like a charge density.Horst
Am 25.06.2017 um 10:25 schrieb EMyrone:
This note derives a completely general set of seven simultaneous differential equations, (16) – (18), (19) – (21) and (23) for seven unknowns, the three Cartesian components of the Q three-vector and the four components of the spin connection four-vector. These can all be expressed as functions of space and time. This is an exactly determined problem in three dimensions. The method uses the two homogeneous field equations of ECE2 gravitation, Eq. (22) and the Faraday law of induction Eq. (9), and the antisymmetry condition (19) to (21). In two dimensions X and Y, there is only one antisymmetry condition (27) and the Faraday law reduces to Eq. (28). Using the Coulomb law of ECE2 gravitation gives Eq. (36). So in the planar limit thee are three equations in five unknowns. The Newtonian limit of Eqs. (30) and (31) is used to give five equations in five unknowns. In the next note the Ampere Maxwell Law of ECE2 gravitation will be introduced into the planar analysis, to seek a general solution without having to assume the Newtonian approximation.