Euler Angles (Z-Y-Z)
The Z-Y-Z Euler angles describe the orientation of a rigid body using three independent
parameters.
The sequence of rotations is as follows:
- Rotate by angle $\alpha$ about the body $Z$ axis.
- Rotate by angle $\beta$ about the new body $Y$ axis (line of nodes).
- Rotate by angle $\gamma$ about the new body $Z$ axis.
Rotation Matrix
The total rotation matrix $R$ is the product of the individual matrices:
$$ R = R_z(\gamma) \, R_y(\beta) \, R_z(\alpha) $$
Where the individual matrices are defined as:
$$ R_z(\theta) = \begin{bmatrix} \cos\theta & -\sin\theta & 0 \\ \sin\theta & \cos\theta & 0 \\ 0 & 0 &
1 \end{bmatrix}, \quad
R_y(\theta) = \begin{bmatrix} \cos\theta & 0 & \sin\theta \\ 0 & 1 & 0 \\ -\sin\theta & 0 & \cos\theta
\end{bmatrix} $$
(You can edit this content later by searching for the "Info Panel" section in the HTML file.)