I think that all is OK. It comes from Eq. (3) of Note 362(5), which I cross checked as in Notes for UFT361 and UFT362. It is precisely this term that is responsible for the transition from particle or classical dynamics to fluid dynamics. You could check it through using Eq. (3) of Note 362(5), which leads to Eq. (5) of that note. Eq. (7) is Eq. (5) in matrix format. The basic idea of UFT362 as you know is to assume that spacetime or the vacuum or the aether is a fluid governed by the ECE2 / Kambe equations of fluid dynamics. The basic idea of fluid dynamics is that the general vector field V is:
V = V(t, r(t), theta(t))
needing the chain rule of differentiation (e.g. “Vector Analysis Problem Solver”). The chain rule leads to the convective, material or Lagrange derivative, a special case of the Cartan derivative as we have just shown. In classical dynamics, V of a particle is V(t).
Sent: 25/11/2016 19:58:32 GMT Standard Time
Subj: Re: FOR POSTING: UFT362 Sections 1 and 2, Orbital Theory in a Fluid Aether
Shouldn’t in eq. (8) in the middle term, rhs, capital and lowercase v be interchanged? To my understanding the operator is
In (22) the Cartan derivative is applied to [r 0]. Shouldn’t this vector also appear in the last term of the rhs?
Am 25.11.2016 um 14:28 schrieb EMyrone:
This paper begins the consideration of orbital theory in a fluid spacetime, aether or vacuum, and shows that the aether or vacuum changes the orbit through the Cartan spin connection. For example an elliptical orbit may be changed into a precessing elliptical orbit by choice of spin connection. This can be considered in future work.