Rotation matrices February 6, 2015Theoryadmin Rotation around the X-axis Rotation around the Y-axis Rotation around the Z-axis
![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]](https://l.wordpress.com/latex.php?latex=%20R_x%28%5Calpha%29%3D%5Cleft%5B%5Cbegin%7Bmatrix%7D1%20%26%26%200%20%26%26%200%20%26%26%200%20%5C%5C0%20%26%26%20cos%28%5Calpha%29%20%26%26%20-sin%28%5Calpha%29%20%26%26%200%20%5C%5C0%20%26%26%20sin%28%5Calpha%29%20%26%26%20cos%28%5Calpha%29%20%26%26%200%20%5C%5C0%20%26%26%200%20%26%26%200%20%26%26%201%5Cend%7Bmatrix%7D%5Cright%5D&bg=FFFFFF&fg=000000&s=1 "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]")
![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]](https://l.wordpress.com/latex.php?latex=%20R_y%28%5Cbeta%29%3D%5Cleft%5B%5Cbegin%7Bmatrix%7D%20cos%28%5Cbeta%29%20%26%26%200%20%26%26%20sin%28%5Cbeta%29%20%26%26%200%20%5C%5C0%20%26%26%201%20%26%26%200%20%26%26%200%20%5C%5C-sin%28%5Cbeta%29%20%26%26%200%20%26%26%20cos%28%5Cbeta%29%20%26%26%200%20%5C%5C0%20%26%26%200%20%26%26%200%20%26%26%201%5Cend%7Bmatrix%7D%5Cright%5D&bg=FFFFFF&fg=000000&s=1 "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]")
![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]](https://l.wordpress.com/latex.php?latex=%20R_z%28%5Cgamma%29%3D%5Cleft%5B%5Cbegin%7Bmatrix%7D%20cos%28%5Cgamma%29%20%26%26%20-sin%28%5Cgamma%29%20%26%26%200%20%26%26%200%20%5C%5Csin%28%5Cgamma%29%20%26%26%20cos%28%5Cgamma%29%20%26%26%200%20%26%26%200%20%5C%5C0%20%26%26%200%20%26%26%201%20%26%26%200%20%5C%5C0%20%26%26%200%20%26%26%200%20%26%26%201%5Cend%7Bmatrix%7D%5Cright%5D&bg=FFFFFF&fg=000000&s=1 "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]")