Rotation matrices

Rotation around the X-axis

x_rotation

 R_x(\alpha)=\left[\begin{matrix}1 && 0 && 0 && 0 \\0 && cos(\alpha) && -sin(\alpha) && 0 \\0 && sin(\alpha) && cos(\alpha) && 0 \\0 && 0 && 0 && 1\end{matrix}\right]

Rotation around the Y-axis

y_rotation

 R_y(\beta)=\left[\begin{matrix} cos(\beta) && 0 && sin(\beta) && 0 \\0 && 1 && 0 && 0 \\-sin(\beta) && 0 && cos(\beta) && 0 \\0 && 0 && 0 && 1\end{matrix}\right]

Rotation around the Z-axis

z_rotation

 R_z(\gamma)=\left[\begin{matrix} cos(\gamma) && -sin(\gamma) && 0 && 0 \\sin(\gamma) && cos(\gamma) && 0 && 0 \\0 && 0 && 1 && 0 \\0 && 0 && 0 && 1\end{matrix}\right]

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