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Help with conversion to index notation

  1. Sep 4, 2012 #1
    1. The problem statement, all variables and given/known data
    Use index notation to calculate the following:

    Let R = u x (d/du)
    hint: R_i = epsilon_ijk u_j (d/du_k)

    R . (u x [T . u])

    where T is a traceless (T_ii = 0), symmetric, and constant (i.e, independant of u) second order tensor. Convert your final result to Gibbs' notation.

    Note:
    . = dot product
    x = cross product
    _ = subscript following


    2. Relevant equations
    (See above problem statement)


    3. The attempt at a solution

    I am having problems converting equations of multiple terms into index notation from Gibbs' notation. I have generally been trying to move from outwards in so thus far I have:

    R_i {u x (T . u)}_i

    from here I am not quite how to handle the two sets of parenthesis inside the second term. My best shot so far has been:

    [epsilon_ijk u_j (d/du_k)] (epsilon_ilm u_l [T . u]_m)

    ...from here I do not know how to handle the conversion of the last T . u term into index notation. Once there I think I can play around with it and hopefully arrive at an answer, but the writing in index notation is really throwing me.

    Anyone out there use index notation?
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
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