It looks as if the assumption of an incompressible, inviscid spacetime is too simple. The conservation of angular momentum is Eq. (19), the vorticity equation. Kambe used an appoximation in which the right hand side is zero, but then, effects due to the Reynolds number are lost.
Time Dependent x and Onset of Turbulence
Equations (7-8) plus (9) or plus the above divergence equation cannot be resolved algebraically for r dot dot, phi dot dot and x dot. Obviously both equation sets are inconsistent.
Concerning the angular momentum, I assume that the simple orbital momentum L is impacted by the fluid dynamics effects so that eq.(9) does not hold in this case.
Am 01.04.2017 um 13:48 schrieb EMyrone:
This note derives the equations (7) to (9) for a time dependent x factor, with x defined in terms of the position field R sub r of UFT363. These equations can be solved for the orbit in terms of x and x dot. In the first instance these can be used as input parameters. It is already known from computation (UFT363) that a constant x gives a precessing orbit, a major discovery. In order to try to solve for x and x dot the assumption can be made of an inviscid, incompressible fluid spacetime governed by Eq. (14). This gives the additional equation (15) which can be solved simultaneously with Eqs. (7) to (9). The conservation of the angular momentum of fluid spacetime gives the vorticity equation (19) in terms of the Reynolds number R of fluid spacetime. At a particular Reynolds number the spacetime become turbulent, and the turbulence will affect the precessing orbit.