This is a rigorously self consistent result, and another important step forward. The relativistic angular momentum is calculated numerically using Cartesian coordinates and is a constant to machine precision. The non relativistic angular momentum is not a constant. The problem of shrinking orbits can be thought out using these methods. The older UFT papers on shrinking used empiricism to a certain extent. I will google around for a system in which initial conditions are defined. This will give a precise comparison of theory and experiment. This is enlightened progress away from the fog of Einsteinian relativity. Everything deduced from the latter theory is totally wrong. By now this conclusion is well known and in fact, well accepted, in the Age of Knowledge. No black holes, no big bang, no gravitational radiation of the Einsteinian variety. If gravitational radiation has been detected, a very big if, it is due to ECE2 relativity, in which radiation theory is the same as in electromagnetism, but many orders of magnitude weaker.
Sent: 10/04/2017 11:06:45 GMT Daylight Time
Subj: Re: Non Relativistic and Relativistic Angular Momenta
Sorry, my data were wrongly denoted, sending over corrected version. The relativistic angular momentum
L = gamma m bold r x bold v
is constant as expected in the relativistic calculation. As you know the angular momentum is calculated a posteriori from the solution of the Lagrange equations. The result is the same for Cartesian and polar coordinates.
It would be very good if you could find initial conditions for a strongly precessing 2-body system. Do we also have a new explanation for the experimentally observed shrinking of orbits? It certainly is not because of gravitational radiation. We did some work on this in older papers.
Am 10.04.2017 um 10:25 schrieb EMyrone:
Many thanks again! The non relativistic angular momentum is a constant of motion but the relativistic angular momentum is not. What does the orbit look like with a relativistic angular momentum? These results are very important because the use only the lagrangian and definition of angular momentum.
Sent: 09/04/2017 15:59:29 GMT Daylight Time
Subj: Re: 375(3): Relativistic Lagrangian in Cartesain Coordinates
PS: This is the non-relativistic and relativistic angular momentum.
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.