Subject: Fwd: Some discussion on Note 124(1)
Date: Mon, 1 Dec 2008 12:56:20 EST
OK thanks, I will develop note 124(2) a bit more tomorrow, using the conventional definition of the angular momentum in a flat orbit. From the Lagrange equation the angular momentum is a constant of motion as is well known. It is
J bold = mvr k = r x p
in the Z axis if the orbit is in the X Y plane, giving Kepler’s second law (Marion and Thornton chapter 7). The angular momentum does not change with time, so:
dJ / dt = 0
which si conservation of angular momentum. So if the stars of a galaxy are in a central orbit around its centre, then fro all types of orbits (Newtonian and non-Newtonian)
del J = 0
and for the galaxy
R = omega T
is therefore also general result. Kepler’s first and third laws are specifically dependent on the inverse square law, but the second law is not (Marion and Thornton, chapter seven).
ok, I will think further about these models and see how they can be solved.
Horst
—–Ursprüngliche Mitteilung—– Von: EMyrone] at [aol.com An: HorstEck] at [aol.com Verschickt: Mo., 1. Dez. 2008, 8:31 Thema: Re: Some discussion on Note 124(1)
I think your ideas are excellent here, feel free to go ahead with them. It may be possible to prepare some preliminary animations to be sent to the animating company. The idea of eq. (7) comes from Atkins (the volume you bought last year), and is a new idea about the nature of angular momentum. However, your approach is also self-consistent and plausible.  As in paper 108 for example the angular momentum is a constant of motion, (i.e. the total angular momentum is conserved, and does not vary with time), but it still has an r dependence in general. As Atkins shows, the vector
Â
                                    r = - r sub Y i + r sub X j
Â
has a zero divergence, but is still r dependent. So this removes the contradiction. I think we should use as many approaches as we can think of, because Fucilla can animate everything we do.
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