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Derivating a velocity's components

  1. Oct 24, 2009 #1
    1. The problem statement, all variables and given/known data

    What is the derivate of the following equation?

    [tex] v(t) = \dot{r}\hat{r} + r \dot{\hat{r}} = \dot{r} \hat{r} + r \dot{\delta} \hat{e}
    [/tex]

    where e is dependent on the angle, delta.


    3. The attempt at a solution

    My answer:

    We know that
    [tex] \hat{r} = \frac {r} {|r|}[/tex]

    => [tex] \hat{r} = \frac {r} {|r|} [/tex]

    => [tex] D( \dot{r} \hat{r} ) = \ddot{r} \hat{r} + \dot{r} \dot{ \hat{r}} [/tex]
    => [tex] D( r \dot{\hat{r}} ) = \dot{r} \dot{\hat{r}} + \frac {r \ddot{r} } {|r|} [/tex]

    so we get

    [tex] a(t) = \hat{r} ( \ddot{r} ) + 2 \dot{r} \dot{ \hat{r}} + \frac {r \ddot{r}} {|r|} [/tex]

    which is wrong.

    The correct answer is

    [tex] \dot{v(t)} = (\ddot{r} - r \dot{\delta}^2) \hat{r} + (r \ddot{\delta} + 2\dot{r} \dot{\delta}) \hat{e}[/tex]
     
  2. jcsd
  3. Oct 25, 2009 #2
    Are you working with vectors or scalars?
     
  4. Oct 25, 2009 #3
    The derivate of a vector is a vector.
    It consists of unit vectors which means that there is too scalars in the unit vectors.
    So I am working with vectors.
     
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