380(4): Complete Solution in Three dimensions.

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.


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