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About coordinate transformation of tensor.

  1. Jul 28, 2012 #1
    note:The tensors in the new coordinates system are represented by X'.
    I have a question about the coordinate transformation of tensor.

    σmn=amianjσ'ij; (1)

    ωpq=apkaqlω'kl; (2)

    In the original coordinates system, we have
    σmn = Dmpnqωpq, (3)

    Substituting Eqs.(1) and (2) into Eq.(3), one obtains,
    amianjσ'ij=Dmpnqapkaqlω'kl (4)

    then,
    σ'ij=amianjapkaqlDmpnqω'kl (5)

    Here is the problem. How was the Eq.(5) obtained from the Eq.(4). I can't really understand, because the items amianjapkaql have changed their position, but their subscript don't change.
    Is there any books talking about that?
    thanks.
     
  2. jcsd
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