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

  1. Jun 18, 2016 #1
    1. The problem statement, all variables and given/known data
    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:

    2. Relevant 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*}

    3. 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?
     
  2. jcsd
  3. Jun 22, 2016 #2

    jedishrfu

    Staff: Mentor

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