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How to get Euler angles

  1. Apr 24, 2012 #1
    I know this is rather trivial question but it's not homework!
    I need this as part of a bigger project.

    What I have to do is rotate my reference frame to another one. I want my new z-axis to be a vector Z=(Z1,Z2,Z3)

    Following the notation of this wikipage:

    all I need to do is compute the Euler angles, however, I don't manage to get Y3 and therefore the last angle, gamma.

    Can you please help?
  2. jcsd
  3. Apr 24, 2012 #2


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    Merely giving your new Z-axis only determines 2 of the 3 Euler angles, since it doesn't tell where your new X and Y axes are. You need to specify at least one of the new X or Y axes to determine the third one - that's why you need Y3. Think of it this way - after you've specified your new Z-axis, you can freely rotate about the new Z-axis. This will leave the new Z-axis unchanged, but will change X and Y.
  4. Apr 24, 2012 #3
    You're right! But sorry if I insist, I just want to get this straight.

    If I only know the new z-axis and x and y could be in directions, although forming an orthonormal system, does this means that I could choose my angle gamma to be any value between 0 and 2pi?
  5. Apr 24, 2012 #4


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