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Math Help - rotation matrices

  1. #1
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    rotation matrices

    Hi, I am trying to find some rotation matrices of R^3.

    So for angle \frac{\pi}{2} and axis e_2 I think the rotation matrix is

    R_{e_2} (\frac{\pi}{2}) = \left(\begin{matrix} cos(\frac{\pi}{2}) &0 &sin(\frac{\pi}{2})\\0 &1 &0\\-sin(\frac{\pi}{2}) &0 &cos(\frac{\pi}{2})\end{matrix}\right) = \left(\begin{matrix} 0 &0  &1\\0 &1 &0\\-1 &0  &0\end{matrix}\right)
    I just used the given rotation matrix in R^3 from the text with no real working out needed. Is this correct?


    Need help on this one:

    For the angle \frac{\pi}{6} and axis containing the vector (1,1,1)^t.

    Not sure how to use the (1,1,1)^t in this question.

    Thanks for any help.
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  2. #2
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    Re: rotation matrices

    I think I have misunderstood what the axis e2 is and I think my working out is wrong.

    Any help would be nice.

    Shelford
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  3. #3
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    Re: rotation matrices

    Anyone have any ideas as to how I should interpret the axis e_2 and use (1,1,1)^t?

    I have thought about this question but still can't get it.

    Thanks

    And sorry for making another post, wanted to edit a previous post but I couldn't.
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  4. #4
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    Re: rotation matrices

    Quote Originally Posted by shelford View Post
    Hi, I am trying to find some rotation matrices of R^3.

    So for angle \frac{\pi}{2} and axis e_2 I think the rotation matrix is

    R_{e_2} (\frac{\pi}{2}) = \left(\begin{matrix} cos(\frac{\pi}{2}) &0 &sin(\frac{\pi}{2})\\0 &1 &0\\-sin(\frac{\pi}{2}) &0 &cos(\frac{\pi}{2})\end{matrix}\right) = \left(\begin{matrix} 0 &0  &1\\0 &1 &0\\-1 &0  &0\end{matrix}\right)
    I just used the given rotation matrix in R^3 from the text with no real working out needed. Is this correct?
    Yes.

    Need help on this one:

    For the angle \frac{\pi}{6} and axis containing the vector (1,1,1)^t.

    Not sure how to use the (1,1,1)^t in this question.

    Thanks for any help.
    This is a much more complicated question, and requires more advanced treatment. The best information I can give you is to go to this website and use that procedure. As you can see, it's a multi-step procedure.
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