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Euler angels

  1. Jan 17, 2010 #1
    1. The problem statement, all variables and given/known data
    What are the Euler's angles corresponding to the rotations of a cube in [tex]\theta[/tex] radians around each of its principal axes



    around the x: [tex]\theta[/tex]=[tex]\theta[/tex]
    [tex]\phi[/tex]=[tex]\psi[/tex]=0

    around z:[tex]\psi[/tex]=[tex]\theta[/tex]=0
    [tex]\phi[/tex]=[tex]\theta[/tex]

    around y:[tex]\phi[/tex]=[tex]\theta[/tex]=[tex]\theta[/tex]
    [tex]\psi[/tex]=-[tex]\theta[/tex]


    is it correct? how can I make it more clear? It's very confusing...
     
  2. jcsd
  3. Jan 22, 2010 #2
    Help me please....
     
  4. Jan 23, 2010 #3
    In order to formalize the solution you can use the rotation matrices: [tex] \hat{R}_x(\alpha) [/tex], [tex] \hat{R}_y(\alpha) [/tex], [tex] \hat{R}_z(\alpha) [/tex] and the matrix which describes the whole Euler's transform:

    [tex]
    \hat{R}(\theta, \phi, \psi) =
    \hat{R}_z(\phi) \hat{R}_x(\theta) \hat{R}_z(\psi) \quad (1)
    [/tex]

    It's easy to get rotation around the x and z axes from (1) and your answers for these cases are right.

    As for y-axis the condition

    [tex]
    \hat{R}(\theta, \phi, \psi) = \hat{R}_y(\alpha)
    [/tex]

    yields

    [tex]
    \theta = -\frac{\pi}{2} - \alpha;
    [/tex]

    [tex]
    \phi = \psi = -\frac{\pi}{2}.
    [/tex]
     
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