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Orthogonality from infinitesimal small rotation

  1. May 27, 2015 #1
    Hello buddies,

    Could someone please help me to understand where the second and the third equalities came from?
    Thanks,

    Page-question-tensor.jpg
     
  2. jcsd
  3. May 28, 2015 #2

    DEvens

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    Education Advisor
    Gold Member

    Um... Ok, it's a little difficult to know what level of detail you want.

    The first equation essentially says that the length of a vector does not change under rotations. The second one follows from the first one using the chain rule, and assuming delta of gik is zero.
     
  4. May 31, 2015 #3
    Thanks for answering,

    gik is basically the inner product of the base set vector, i.e., <ei,ek>.
    - Could you please explicit the chain rule?
    - is vik time dependent? And since it is an infinitely small matrix, the ##\delta v^k_i = I##?

    Thanks
     
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