Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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


    User Avatar
    Science Advisor

    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


    User Avatar
    Science Advisor

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook