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Finding Euler angles from rotation about arbitrary axis

  1. Apr 15, 2013 #1
    1. The problem statement, all variables and given/known data

    An object is rotated 45 degrees about an axis whose + direction is that of (i-k). Find zxz Euler angles (that is, Euler angles as introduced by Goldstein) for a set of three active rotations that gives the same net motion of the object.


    2. Relevant equations

    Goldstein chapter 4, eq 4.46. Not sure how to input it here.

    3. The attempt at a solution
    What I tried to do was to find the rotation matrix corresponding to the rotation about the given axis using the Rodriguez rotation formula http://en.wikipedia.org/wiki/Rotation_matrix#Rotation_matrix_from_axis_and_angle, and then compared to eq. 4.46 in Goldstein and get the Euler angles that way. But the problem specifies to find rotation of the object, and eq 4.46 describes the rotation of the axes. How can I find the Euler angles that describes the rotation of the object, not the axes? Was my approach the indicated/correct or is there another way?
    Also, Can someone explain to me was is the meaning of eq 4.47 (the transpose of that matrix)
    Thanks.
     
  2. jcsd
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