Question on the 3D Kinematics equation.

[kwnmanu94]

How exactly did the terms in parenthesis of the equation (14) become (15)?

I don't even know what the Transport Theorem is about?

 

[Filip Larsen]

What textbook is this? Since the text directly references Transport Theorem I would expect it to be described earlier. Perhaps look in the index or try compare with transport theorem where you can see it relates the coordinate-wise time derivative of a point coordinated by two different coordinate system that rotate relative to each other.

 

[robphy]

https://ocw.mit.edu/courses/2-003sc...c8efae261114febe1f_MIT2_003SCF11Kinematic.pdf
Your diagram is on page 5.
The transport theorem is on page 4,
whose section is entitled
"2.2 Taking Derivatives using Angular Velocity and the Transport Theorem"