Rotation Matrices

Rotation along θ

θ (Theta)

Decimal Places

Radians

R_x(\theta) =\egin{vmatrix}1 &0 &0 \\0 &cos \theta &-sin \theta \\0 &sin \theta &cos \theta\end{vmatrix}

R_x(0 ) =\egin{vmatrix}1 &0 &0 \\0 &1 &0 \\0 &0 &1\end{vmatrix}

R_y(\theta) =\egin{vmatrix}cos \theta &0 &sin \theta \\0 &1 &0 \\-sin \theta &0 &cos \theta\end{vmatrix}

R_y(0 ) =\egin{vmatrix}1 &0 &0 \\0 &1 &0 \\0 &0 &1\end{vmatrix}

R_z(\theta) =\egin{vmatrix}cos \theta &-sin \theta &0 \\sin \theta &cos \theta &0 \\0 &0 &1\end{vmatrix}

R_z(0 ) =\egin{vmatrix}1 &0 &0 \\0 &1 &0 \\0 &0 &1\end{vmatrix}

θ (Theta X)

θ (Theta Y)

θ (Theta Z)

Decimal Places

Radians

R_{x}(\theta) =\egin{vmatrix}1 &0 &0 \\0 &1 &0 \\0 &0 &1\end{vmatrix}

R_{y}(\theta) =\egin{vmatrix}1 &0 &0 \\0 &1 &0 \\0 &0 &1\end{vmatrix}

R_{z}(\theta) =\egin{vmatrix}1 &0 &0 \\0 &1 &0 \\0 &0 &1\end{vmatrix}

R_{xyz}=R_{z} \cdot R_{y} \cdot R_{x} =\egin{vmatrix}1 &0 &0 \\0 &1 &0 \\0 &0 &1\end{vmatrix}

R_{xzy}=R_{y} \cdot R_{z} \cdot R_{x} =\egin{vmatrix}1 &0 &0 \\0 &1 &0 \\0 &0 &1\end{vmatrix}

R_{yxz}=R_{z} \cdot R_{x} \cdot R_{y} =\egin{vmatrix}1 &0 &0 \\0 &1 &0 \\0 &0 &1\end{vmatrix}

R_{yzx}=R_{x} \cdot R_{z} \cdot R_{y} =\egin{vmatrix}1 &0 &0 \\0 &1 &0 \\0 &0 &1\end{vmatrix}

R_{zxy}=R_{y} \cdot R_{x} \cdot R_{z} =\egin{vmatrix}1 &0 &0 \\0 &1 &0 \\0 &0 &1\end{vmatrix}

R_{zyx}=R_{x} \cdot R_{y} \cdot R_{z} =\egin{vmatrix}1 &0 &0 \\0 &1 &0 \\0 &0 &1\end{vmatrix}