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Orthogonality of time dependent vector derivatives of constant magnitude

  1. Aug 31, 2010 #1
    I'm having trouble understanding why a derivative of a time dependent vector function is orthogonal to the original function. Can anybody give me some enlightenment? I searched around for some previous talk about this, and I can't find anything.

    Thanks.
     
  2. jcsd
  3. Sep 2, 2010 #2
    You have to be a bit more specific... I don't understand your question right now.
     
  4. Sep 2, 2010 #3

    George Jones

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    Does the time-dependent vector have constant magnitude?
     
  5. Sep 2, 2010 #4
    Yes the original vector function is of constant magnitude. Take a vector function r(t) of constant magnitude and then r dot should be orthogonal to r. I don't understand why.
     
  6. Sep 3, 2010 #5

    George Jones

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    Take the derivative with respect to time of both sides of

    [tex]r^2 = \bold{r}\left( t \right) \cdot \bold{r}\left( t \right).[/tex]

    What do you get?
     
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