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I Rotation matrix in 3x3

  1. Nov 1, 2016 #1
    Hello! I need to find the rotation matrix around a given vector v=(a,b,c), by and angle ##\theta##. I can find an orthonormal basis of the plane perpendicular to v but how can I compute the matrix from this? I think I can do it by brute force, rewriting the orthonormal basis rotated by ##\theta## and doing some matrix multiplications, but is there a more clever and fast way to do it?
    Thank you!
     
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  3. Nov 1, 2016 #2

    Erland

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    I don't think there is any simpler method than "brute force".
     
  4. Nov 1, 2016 #3

    Filip Larsen

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    You might want to research Rodrigues' rotation formula.
     
  5. Nov 1, 2016 #4

    mathwonk

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    I guess this is what you are saying but the obviopus way to prceed seems to me to use the basis you have as a map sending the usual orthonormal basis to the new one, and use that map and its inverse to conjugate the (easily written) rotation about the z axis back to your axis.
     
  6. Nov 3, 2016 #5

    jasonRF

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