Why is velocity in body fixed frame equals to angular veloc?

[AntoineCompagnie]

Homework Statement

I don't understand, physically speaking, how do we get from the first equation to the second: how do we get the fact that velocity in body fixed frame equals to angular velocity in body fixed frame.

Furthermore I dont' understand how we get the angular velocity in inertial frame:

Homework Equations

\begin{align*}\underbrace{\dot q}_{\text{Velocity in inertial frame}}&=\underbrace{\dot R p}_\text{Position in body fixed frame}:\hat \omega^b\ \text{This okay for me}\\
\underbrace{R^T\dot q}_{\text{Velocity in body fixed frame}}&=\underbrace{R^T\dot R p}_\text{Angular velocity in body fixed frame}\text{I don't understand}\end{align*}

the angular velocity in inertial frame

\begin{align*}\underbrace{\dot q}_{\text{Velocity in inertial frame}}&=\underbrace{\dot R R^Tq}_\text{angular velocity in inertial frame}:\hat \omega^s \ \text{I don't understand}
\end{align*}

The Attempt at a Solution

My callsmate told me in the bus that he wasn't sure if my equations were quite right...Can you help me understand these equations?

 

[jedishrfu]

This reference may help:

http://physics.stackexchange.com/questions/88398/why-is-body-frame-angular-velocity-nonzero

and this may be more than you asked for:

http://www.physics.indiana.edu/~dermisek/CM_13/CM-5-2p.pdf