I have a 3D point that is rotated about the $x$-axis and after that about the $y$-axis. I know the result of this transformation. Is there an analytical way to compute the rotation angles?
$ v'=R_y(\beta)*R_x(\alpha)*v $ Here, $v$ and $v'$ are known and I want to compute $\alpha$ and $\beta$. $R_x$ and $R_y$ are the rotation matrices about the x and y axis respectively. The overall matrix will then be:
$ R=\begin{pmatrix} \cos \beta & \sin\alpha * \sin\beta & \cos\alpha * \sin\beta \\ 0 & \cos \alpha & -\sin\alpha \\ -\sin\beta & \cos\beta * \sin\alpha & \cos\alpha * \cos\beta \end{pmatrix} $