Many thanks again. This is just a typo, the equation should be the same as Eq. (25) of UFT270. The rest of the note is the same. The great advantage of UFT371 over UFT270 is that Maxima is able to solve all the relevant equations numerically in UFT371, so the laborious hand calculations in UFT270 no longer have to be done. A close control over the use of the computer is still needed of course, but an array of new possibilities opens up. I will proceed now to develop the same problem in terms of the Eulerian angles. ECE2 relativity is still needed of course in other situations, but it would be interesting to see whether classical rotational dynamics gives planetary precessions. That would mean that one of the most famous experiments of Einsteinian general relativity EGR, the precession of the perihelion, would be refuted. We have refuted EGR in many ways, and there have been no valid objections to these refutations. The lagrangian (1) of Note 371(1) gives precessions in the angles of the spherical polar coordinates. When Eulerian angles are used, more precessions appear on the classical level. Furthermore, we now know clearly that classical rotational dynamics are governed by a well defined spin connection of Cartan geometry. Finally, all these calculations can be quantized. Again, Maxima removes all the laborious calculations.
Sent: 22/02/2017 13:48:28 GMT Standard Time
Subj: Re: Note 371(1): Precession of the Perihelion on the Classical Level
Anything seems to go wrong with beta. Inserting beta dot squared from (6) does not give (1), there are additional terms then.
Am 21.02.2017 um 12:31 schrieb EMyrone:
This note looks afresh at the precession of the perihelion by setting up the classical lagrangian (1) and solving Eqs. (3), (4), (5), (9) and (13) simultaneously for the orbit r = alpha / (1 + epsilon cos beta) where beta is defined in Eq. (6). This method is a development of one used originally in UFT270. The power of the Maxima program now allows the relevant equations to be solved for beta in terms of the angles theta and phi if the spherical polar coordinates system. There are precessions in theta and phi. The precession of the perihelion is usually thought of as a precession of phi in a planar orbit, using the incorrect Einsteinian general relativity. In the UFT papers ECE2 relativity has been used to describe the precession. However it may be that it can be described on the classical level with the use of spherical polar coordinates. If this supposition is true, and if Eq. (8) is a precessing ellipse, then other precessions can also be developed in this way. The theory can also be developed with the Eulerian angles. In general there are precessions in theta and phi. There is no reason why an orbit should be planar. In general it must be described by a three dimensional theory.