These results are again full of interest and can be written up in Section 3 of UFT374. This Cartesian approach is the one with which most people are familiar. A lot of people get confused with the use of a coordinate system in which the frame itself is moving, for example the plane polar and spherical polar systems. Without the fluid dynamic terms the cartesian method does not even give the centrifugal force, as is well known, but the addition of fluid gravitational terms gives a precessing ellipse. This is a remarkable achievement, and congratulations. I have just sent over the lagrangian for fluid dynamics, which is capable of giving many types of orbit. Therefore it has been shown here that a Cartesian analysis in fluid gravitation makes the Einstein theory completely redundant. Only the most dogmatic and ostrich minded can ignore all the refutations and advances.
Sent: 06/04/2017 09:31:37 GMT Daylight Time
Subj: Re: A direct approach to mass point dynamics in a fluid
A general velocity field (vfx, vfy) has been added in the kinetic energy terms. Then the most general Euler-Lagrange equations then are:
For a constant vf there is no change in the equations of a masspoint without fluid velocity, that means such a case is contained in appropriate initial conditions. By defining any form of vf one can obtain various orbit types as I found in the ECE2 fluid dynamics case. For example
gives a rosette which is a precessing ellipse with large precession angle, see Fig. 6. The precession can be minimized by a0 –> 0.
Am 05.04.2017 um 09:11 schrieb Horst Eckardt:
What about the following approach (in cartesian coordinates):
Given: a velocity field bold vf(X,Y,Z,t)
Coordinates of mass point: X,Y,Z
velocity of mass point:
bold v = (v_X + vf_X, v_Y + vf_Y, vZ + vf_Z)
with v_X = X dot, etc.
The Lagrange equations can be obtained from the above equation for bold v. It has to be checked if this is a valid precedure because in Lagrange theory normally the coordinates are transformed and not the velocities. As an alternative, one could certainly solve Newton’s equations directly.
This model does not include viscosity or other additional effects.