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Math Help - Einstein indicial notation problem

  1. #16
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    Re: Einstein indicial notation problem

    Quote Originally Posted by milad View Post
    thanks .I will try to do the same in 3D .
    You're welcome. It works in 3d, but too much to post.
    Thanks from milad
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  2. #17
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    Re: Einstein indicial notation problem

    A2ik means each member powered to 2 . Aij*Ajk=A2ik is true only if A is a diagonal tensor .which I think you didn't notice . thank you so much for your time and effort .
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  3. #18
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    Re: Einstein indicial notation problem

    Quote Originally Posted by milad View Post
    A2ik means each member powered to 2 . Aij*Ajk=A2ik is true only if A is a diagonal tensor .which I think you didn't notice . thank you so much for your time and effort .
    It does not. A2ik means the ik component of A2.

    A = laijl and Aij, the ij component of A, is aij.
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  4. #19
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    Re: Einstein indicial notation problem

    I showed the answer to my professor but he says I must do all the work in index notation .
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  5. #20
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    Re: Einstein indicial notation problem

    Quote Originally Posted by milad View Post
    I showed the answer to my professor but he says I must do all the work in index notation .
    With principal directions in 3d

    (s112+s222+s332)2 = s114+s224+s334 + 2(s112s222+ s112s332+ s222s332)

    (s11+s22+s33)2 = s112+s222+s332 + 2(s11s22+ s11s33+ s22s33) = 0 because sii=0. So
    s112+s222+s332 = -2(s11s22+ s11s33+ s22s33)

    (s112+s222+s332)2 = 4[s112s222+s112s332+s222s332 + 2(s11+s22+s33)(s11s22s33)] and sii=0. So
    s112s222+s112s332+s222s332 = (s112+s222+s332)2 and substitute this into first eq to get:

    s114+s224+s334 = (s112+s222+s332)2 , or in indicial notation:

    sii4 = sii2sjj2

    The above in indicial notation is:

    (sii2)2 = sii4 + 2A
    (sii)2 = sii2 + 2B = 0
    sii2 = -2B
    (sii2)2 = 4B2 = 4A, if you can show B2 = A
    Then
    sii4 = sii2sjj2

    I cant express things like s11s22+ s11s33+ s22s33 in indicial notation.
    Surely your Prof at some point has to show you how to do this problem in indicial notation.
    Please let us know.

    EDIT: Had to juggle with Latex help again to get my Word sub-super script version to post.
    Last edited by Hartlw; April 30th 2013 at 10:08 AM.
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