Equations of motion from dH/dt=0, dL/dt=0

Equations of motion from dH/dt=0, dL/dt=0

I do not think that there is any problem, because dH / dt has already been worked out by computer in both (r1, phi) and (r, phi) in UFT417 – UFT419. I have also checked that the lagrangian and hamiltonian methods give exactly the same result in the limit m(r1) goes to 1. So Eq. (4) of Note 420(5) must give the same result as that already obtained by computer algebra in UFT417 – UFT419. So we can just run Eq. (4) of Note 420(5) through Maxima in the coordinate system (r1, phi), then in the coordinate system (r, phi), and finally in the Cartesian system and isolate the vacuum force in each case. I can go through Note 420(5) again by hand using the three coordinates systems, but the computer is obviously the better method.

Equations of motion from dH/dt=0, dL/dt=0

I used eqs.(21) and (24) of note 420(3) to compute the expressions

dH/dt = 0
dL/dt = 0

in polar coordiantes of r_1 space. I used the form m(r_1) consequently,
not the form m(r). It is not clear if always the correct distinction of
r and r_1 is made in the note. This may be a source of confusion.
The final results o17, o18 in the protocol are the combined equations of
motion. There is no classical term

– phi dot r_1 dot / r_1

for phi dot dot. Please check if the initial approaches are correct. I
gues that anything went wrong.

Horst

420(6a).pdf

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