# Convert from Rotation Matrix to Fixed-Axis (Extrinsic) zxz Euler Angles

How can an arbitrary rotation matrix

$R = \left(\begin{matrix} R_{11} & R_{12} & R_{13} \\ R_{21} & R_{22} & R_{23} \\ R_{31} & R_{32} & R_{33}\end{matrix}\right)$

be decomposed into the equivalent fixed-axis zxz Euler angles ($\theta,\phi,\psi$)?

I understand the decomposition into the equivalent body-axis Euler angles, but I don't follow the decomposition for the fixed-axis situation.

• If you have the body-axis set of angles, then you just need to reverse the sequence of rotations to get the correct angles in the extrinsic axes. Since you're using a set of rotations that uses the same axes backwards or forwards, that should be no problem. – Muphrid Oct 2 '15 at 4:49
• Awesome, thanks. Didn't realize it was that easy. – bucmipid-153 Oct 4 '15 at 18:40