Euler Angles ‐ Direct and Inverse Problems

Problem 1

Find the rotation matrix corresponding to the set of Euler angles $ZXZ$. Solve the inverse problem.

Problem 2

Discuss the inverse solution for the Euler angles $R(\varphi, \vartheta, \psi) = R_z(\varphi) \cdot R_{y'}(\vartheta) \cdot R_{z''}(\psi)$ in the case $s_{\vartheta} = 0$.