I know how to find out if an infinitesimal delta is of the first order (if \frac{\delta y}{\delta x}=\frac{dy}{dx}+\epsilon\approx\frac{dy}{dx}\deltax, but how do you find out if an infinitesimal is of second order or higher and how do you find out what that order is?
You are taking the material derivative because the volume is a material fluid (a function of initial position and time where there is no flux of mass) as opposed to a control volume which is just a function of position with a fixed volume. Basically, you can still use the transport theorem on a...
Yes, it is if f is a scalar field. But in the Reynolds transport theorem, f is a vector field. For a vector field V, the material derivative is defined as follows:
\begin{equation} \frac {Df} {Dt} = \frac {\partial V} {\partial t} + (\mathbf V \cdot \nabla) V \end{equation}
I know how to find out if an infinitesimal delta is of the first order (if delta*y/delta*x=dy/dx+epsilon is approximately equal to (dy/dx)*delta*x, but how do you find out if an infinitesimal is of second order or higher and how do you find out what that order is?
Note: I will update this...
\begin{equation} \frac {Df} {Dt} \end{equation} is just the material derivative (the derivative with respect to time while keeping the initial position constant).
I eventually came to the same conclusions about the term space structure referring to a coordinate system. I know I did not quote completely accurately, in fact I didn't quote at all, merely tried my best to summarize the author's unrelativistic and apocryphal views towards the speed of light. I...
The article was in the book "Advanced Theory of Relativity" by Peter Lay. The author used the term to refer to a part of space in one frame of reference from which time dilation decreases or increases the apparent speed of light from the viewpoint of an observer. Not sure if this is just the...
What is a "Space Structure" in relativity?
I remember reading an article that said essentially that the point of reference and the number of "space structures" affect the speed of light. Is this a popular theory? What is a space structure in physics anyway, I'm pretty well versed in physics and...