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Orthogonal Tensor Proof

  1. Sep 30, 2008 #1
    I'm curious as to how the following proof is verified. I have toiled over this thing for quite a while, but haven't made any progress. I don't need a step-by-step solution, but I would appreciate any help getting it started:

    Given the following:

    Q is an orthogonal tensor
    e1 is a unit vector such that Qe1 = e1
    n is of unit length and orthogonal to e1
    m is such that m[tex]\bullet[/tex]e1 = 0, m = Qn and m[tex]\bullet[/tex]n= cos[tex]\theta[/tex]
    1 is the identity matrix

    Prove that:

    Q = 1cos[tex]\theta[/tex] + (1-cos[tex]\theta[/tex])e1[tex]\otimes[/tex]e1 - (e2[tex]\otimes[/tex]e3-e3[tex]\otimes[/tex]e2)sin[tex]\theta[/tex]

    Where e1, e2, and e3 form an orthonormal triad and
    [tex]\otimes[/tex] represents the dyadic product

    My apologies if this is the wrong thread to post this at, but I looked around and couldn't find any threads on this topic.
  2. jcsd
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