Question

mechanics

Answer 1

XYZ is the fixed system of coordinates and
xyz is the time-varying system of coordinates
Given
\[\vec A=A_{1}i+A_{2}j+A_{3}k\]
Also given
\[\frac{d \vec A}{dt}|_{f}=\frac{d \vec A}{dt}|_{m}+\vec \omega \times \vec A\]
where
\[\frac{d \vec A}{dt}|_{f}\]
and
\[\frac{d \vec A}{dt}|_{m}\]
are time derivatives of vector A with respect to the fixed and variying system of coordinates respectively

Now the part I don't understand is
Let \[D_{f}\] and \[D_{m}\] be symbolic time derivative operators in the fixed and moving systems respectively. Demonstrate the operator equivalence
\[D_{f} \equiv D_{m} + \vec \omega \times\]
What is the triple equal sign and where is there an unecessary cross next to omega?