414(1): Summary of the Orbit Shrinking Equations

OK thanks for confirming that the simultaneous numerical solution of Eqs. (1) and (12) gives a shrinking and precessing orbit. In my opinion this is another important result, which makes EGR completely irrelevant and obsolete. The hamiltonian must be a constant of motion for any conservative system in dynamics, so dH / dt = 0 and dL / dt = 0. It is known that dH / dt = 0 leads back to Eqs. (1) and (12). I could write out this proof in the next note. as t goes to infinity the spin connection in Eq. (8) remains finite, so Eq. (1) does not diverge as t goes to infinity. Also, as t goes to infinity the right hand side of Eq. (12) is zero. So as t goes to infinity the dynamics adjust themselves in such a way that there is no divergence. In Newtonian dynamics phi’ dot = phi dot, and phi dot can become very large for an orbit in which the separation r between m and M is very small. The frame for Newtonian dynamics is ( r , phi). The Newtonian hamiltonian is H = – mMG / a where a is the semi major axis. If the semi major axis of the elliptical Newtonian orbit is very small then H goes to infinity but dH / dt = 0. In the Newtonian case H is the total energy, which is always constant. The total energy can approach infinity in an orbit where a approaches zero, but dH / dt = 0 under all conditions. Exactly the same considerations apply in the frame ( r , phi’).

414(1): Summary of the Orbit Shrinking Equations

The Hamiltonian (15) contains phi dot ‘. According to (10), this variable diverges, if omega_1 –> infinity. Shouldn’t then the Hamiltonian (15) diverge too?

Horst

Am 03.09.2018 um 14:25 schrieb Myron Evans:


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