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Vector analysis

  1. Nov 29, 2008 #1
    hi there!

    I´m doing vector analysis the last two weeks and I feel unsure about this identity. Can anyone of you say if I´m on the right way, and if not where my mistakes lie :)

    [tex]A_i(\vec r)=\sum_{j=1}^3R_{ij}x_j[/tex], R constant 3x3 matrix

    I have to calculate [tex]rot\vec A[/tex], [tex]rotrot\vec A[/tex]

    [tex]rot\vec A=\epsilon_{jki}\partial_j(\sum_{j=1}^3R_{ij}x_j)_k=\epsilon_{jki}\partial_j(R_{ik}x_k)=R_{ik}\epsilon_{jki}\partial_jx_k[/tex]

    [tex]rotrot\vec A=\epsilon_{lkm}\partial_l(R_{ik}\epsilon_{jki}\partial_jx_k)_k=\epsilon_{lkm}\partial_lR_{ik}\epsilon_{jki}\partial_jx_k=\epsilon_{kml}\epsilon_{kij}R_{ik}\partial_l\partial_jx_k=(\delta_{mi}\delta_{lj}-\delta_{mj}\delta_{li})R_{ik}\partial_l\partial_jx_k=R_{mk}\partial_l^2x_k-R_{lk}\partial_l\partial_mx_k[/tex]

    and one more question: consider the scalar:

    [tex]\phi(\vec r)=\sum_{i,j=0}^3Q_{ij}x_ix_j[/tex], Q 3x3 constant

    is this the correct k-th component of the sum:

    [tex]???(\sum_{i,j=0}^3Q_{ij}x_ix_j)_k=Q_{kj}x_kx_j=Q_{ik}x_ix_k ???[/tex]

    thanks a lot in advance!
  2. jcsd
  3. Dec 1, 2008 #2
    any comments are welcome :)
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