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Dot product of derivatives

  1. Apr 5, 2009 #1

    Nabeshin

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    In reading a book on astrodynamics I came across the following statement:
    [tex]\vec{a}\cdot \vec{\dot{a}}=a \dot{a}[/tex]

    Where the dotting is the time derivative notation.

    I put a picture of the original text up, and it's the statement right in the middle:
    http://img.photobucket.com/albums/v715/deagleman9/IMG_1178.jpg
    Except they use bold to indicate vectors.

    Can anyone explain to me why this should be true? It seems akin to saying the angle between a vector and its time derivative is always 90, which is obviously not true. I've also considered it might be a notational problem with the unbolded quantities. At any rate, does anyone know what's going on here?
     
  2. jcsd
  3. Apr 6, 2009 #2

    Nabeshin

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    Never mind, I think I figured this one out. I think the right side is the time derivative of the magnitude of a, rather than the magnitude of the time derivative of a.
     
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