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Integral of vector expression

  1. Jun 20, 2008 #1
    [tex]
    \int [a(\dot{b}\cdot a + b\cdot\dot{a}) + \dot{a}(b\cdot a) - 2(\dot{a}\cdot a)b - \dot{b}|a|^2]\, dt
    [/tex]

    The above are all vectors. How would one go about integrating this, the answer is apparently

    [tex]
    a \times (a \times b) + h
    [/tex]

    where h is a constant vector

    I don't quite see how they arrive at this answer...
     
  2. jcsd
  3. Jun 21, 2008 #2

    tiny-tim

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    p x (q x r) = q(p.r) - r(p.q)

    Hi Ceres629! :smile:

    Easy-peasy … use the standard vector triple-cross-product formula:

    p x (q x r) = q(p.r) - r(p.q), and then differentiate carefully! :smile:
     
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