Many thanks! This is another very important result. It is possible to obtain orbital precession in Cartesian coordinates with the ECE2 lagrangian, making Einsteinian general relativity redundant. It is also very interesting to see that the relativistic angular momentum is not a constant of motion in Cartesian coordinates. The non relativistic angular momentum is a constant of motion both for Cartesian and plane polar coordinates. The relativistic angular momentum is
L = gamma L0
where gamma is the Lorentz factor and L0 the classical non relativistic angular momentum. This can be coded in to find its effect on the orbit. I can google around to try to find the optimal experimental data for comparison. I found one such system where m orbits M with a precessions about thirty degrees per orbit, compared with fractions of seconds of arc in the solar system.
To: EMyrone@aol.com
Sent: 09/04/2017 16:00:14 GMT Daylight Time
Subj: Re: 375(3): Relativistic Lagrangian in Cartesain CoordinatesFor strong relativistic effects, we obtain a precessing ellipse also in Cartesian coordinates as expected, see Fig. 1. Please notice that eq.(6) of the note only holds in the non-relativistic case. This term for L is not constant, see Fig. 2.
Horst
Am 09.04.2017 um 15:53 schrieb EMyrone:
This is given by Eq. (1), and simultaneous numerical solution of Eqs. (3), (4) and (6) should be a precessing ellipse.