Notes 365(1-3)

Thanks in turn!

In a message dated 28/12/2016 12:22:47 GMT Standard Time, mail@horst-eckardt.de writes:

ok, thanks, will work out the graphics as soon as my other computer is working again.

Horst

Am 26.12.2016 um 09:00 schrieb EMyrone:

Many thanks and very interesting. An elegant derivation of Eq. (3) of Note 365(2). The only comment I have is that the derivation is based on the assumption in Eq. (33) of UFT363 that partial R (t, r, theta) / partial theta = 0. This was made to reduce complexity and to give Eq. (3) of Note 365(3), in which:

partial R(t, r, theta) / partial r = f(r, t)

within the approximation in Eq. (33) UFT363.

To: Emyrone
Sent: 24/12/2016 11:33:12 GMT Standard Time
Subj: Notes 365(1-3)

I tried a direct solution of eq.(44) of note 365(1). Using the substitution

u = 1/r

I obtained directly eq.(3) of note 365(3) when inserting suitable
integration constants, see section 2 of the protocol.
A direct solution with variable r gives a similar result but with phase
factors, see eq. o8 (section 1). Trying a theta-dependent function
Omega(theta) gives no analytical solution (section 3).

I am not sure if Omega can be assumed not to depend on theta. According
to eq.(33) of the first note, bold R depends on theta, therefore

partial R / partial r

maintains this dependence. If Omega is not constant, then

f(theta) = 1 / sqrt(1+Omega)

reflects this dependence even by the indirect dependence
Omega(r(theta)), see eqs. 12-14 in note 2.

I will try an example for f(theta) based on the numerical results of
paper 328.

Horst