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

  • #1

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?
 

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