The definitions of orbits with kappa’s is very interesting, precisely what I had in mind, in your phrase “Aether engineering”. In 378(5) I began working with the field potential relations and derived the kappa vectors, tetrads and spin connections. The remarks about the tangent space and base manifold are also very interesting.
To: EMyrone@aol.com
Sent: 26/05/2017 16:15:58 GMT Daylight Time
Subj: Re: 378(2): Field and Force Equations for Any Orbit: Aether EngineeringThe kappa’s can be introduced in eqs.(27,28) and (29,30), but they are constrained by (22,23). Therefore there is no free choice of these. One can however use these equations to define initial conditions. Besides the position of the orbit, the total energy is affected, so it is possible to define a closed or open orbit by suitable kappa’s. The precession is impacted indirectly. If the orbit is smaller, the relativistic effects are larger.
Eqs. (34,35) are interesting from a geometrical standpoint. The geometry is underdetermined by the kappa’s, but assuming the omega’s being zero, we could assume a diagonal tetrad matrix:
q_XX = r(0)/2 * kappa_X
q_YY = r(0)/2 * kappa_Y.This means that the tangent space is defined completely by the orbit when the base manifold is given (for example cartesian). A nice example that Cartan geometry is nothing else than defining coordinate transformations.
Horst
Am 20.05.2017 um 14:57 schrieb EMyrone:
This note shows that the relevant field equations of ECE2 gravitation, Eqs. (13) and (14), reduce to the simple equation (12), which implies Eqs. (22), (23) and (24). Any Newtonian orbit can be aether engineered using Eqs. (27) and (28), with the kappa vector components as input parameters. Any ECE2 retrograde precession can be aether engineered from Eqs. (29) and (30), and any ECE2 forward precession can be aether engineered using Eqs. (31) and (32). The structiure of the kappa vector was given in UFT318, and is defined in Eqs. (33) to (34) in terms of the tetrad vector q bold, spin connection vector omega bold and the length parameter r(0). These are the engineering variables. It ought to be possible to reproduce any observable orbit, and any obsrevable precession. For example a two or three variable least means squares fit to any orbit can be used. I used this type of method in the far infra red in the early Omnia Opera papers, using a NAG least mean squares routine on an Elliott 4130 mainframe with 48 kilobytes of total memory and packs of cards. The Algol code is on www.aias.us So now it should be possible to implement such a method on any desktop using Maxima. The latter can also check the hand algebra as usual, and integrate the equations.