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Matrix of a Rotation Tensor

  1. Mar 2, 2012 #1
    1. The problem statement, all variables and given/known data

    Write the matrix of a rotation tensor corresponding to the rotation by angle θ about an axis aligned with e1+e2

    2. Relevant equations

    I know that the matrix for a rotation tensor about e3 is;

    cosθ -sinθ 0
    sinθ cosθ 0
    0 0 0


    3. The attempt at a solution

    I assume that the rotation would be changing only on the e3 axis because the axis are aligned with e1+e2, right? So the matrix will be all zero with the R33 component being some complicated rotated value?
     
    Last edited: Mar 2, 2012
  2. jcsd
  3. Mar 2, 2012 #2

    tiny-tim

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    hi samee! :smile:

    (try using the X2 button just above the Reply box :wink:)

    how about rotating e1+e2 onto e1, then rotating through θ, then rotating e1 back again onto e1 +e2 ? :wink:
     
  4. Mar 2, 2012 #3
    Okay! I had some new revelations.

    I know that (R-I)u=0 where R is the rotation tensor, I is Identity and u is some vector, here it's e1+e3.

    So, this equation will be true if the R matrix is;

    0 1 0
    1 0 0
    0 0 1

    BUT!!!! I think it needs to be in sinθ and cosθ instead of 1.... right?

    Also- thanks for the tip on the X2 ^_^
     
  5. Mar 2, 2012 #4

    tiny-tim

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    erm :redface:

    the determinant of that is -1 :biggrin:
     
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