EulerAngleSequences 2005-03-03 18:54:43 2005-03-04 11:20:50 Definition A list of the Euler angle rotation matrics for different sequences 1-2-3 $$ \left[ \begin{array}{ c c c } c_2 c_3 & s_1 s_2 c_3 + s_3 c_1 & -c_1 s_2 c_3 + s_3 s_1 \\ -c_2 s_3 & -s_1 s_2 s_3 + c_3 c_1 & c_1 s_2 s_3 + c_3 s_1 \\ s_2 & -s_1 c_2 & c_1 c_2 \end{array} \right] $$ 2-1-3 $$ \left[ \begin{array}{ c c c } c_3 c_1 + s_1 s_2 s_3 & s_3 c_2 & -s_1 c_3 + s_3 s_2 c_1 \\ -s_3 c_1 + c_3 s_2 s_1 & c_3 c_2 & s_3 s_2 + c_3 s_2 c_1 \\ c_2 s_1 & -s_2 & c_2 c_1 \end{array} \right] $$ 3-2-1 $$ \left[ \begin{array}{ c c c } c_2 c_1 & s_1 c_2 & -s_2 \\ s_2 s_3 c_1 - c_3 s_1 & s_1 s_2 s_3 + c_3 c_1 & c_2 s_3 \\ s_2 c_3 c_1 + s_3 s_1 & s_2 c_3 s_1 - s_3 c_1 & c_2 c_3 \end{array} \right] $$ 3-1-3 $$ \left[ \begin{array}{ c c c } c_3 c_1 - c_2 s_3 s_1 & c_3 s_1 + c_2 s_3 c_1 & s_2 s_3 \\ -s_3 c_1 - c_2 c_3 s_1 & -s_3 s_1 + c_3 C_1 & s_2 c_3 \\ s_2 s_1 & -s_2 c_1 & c_2 \end{array} \right] $$ 3-2-3 $$ \left[ \begin{array}{ c c c } -s_3 s_1 + c_2 c_3 c_1 & c_2 c_3 s_1 + s_3 c_1 & -s_2 c_3 \\ -c_2 s_3 c_1 - c_3 s_1 & c_3 c_1 - c_2 s_3 s_1 & s_2 s_3 \\ s_2 c_1 & s_2 s_1 & c_2 \end{array} \right] $$ 2-3-2 $$ \left[ \begin{array}{ c c c } -s_3 s_1 + c_2 c_3 c_1 & s_2 c_3 & -s_3 c_1 - c_2 c_3 s_1 \\ -s_2 c_1 & c_2 & s_2 s_1 \\ c_3 s_1 + c_2 s_3 c_1 & s_2 s_3 & c_3 c_1 - c_2 s_3 s_1 \end{array} \right] $$ 1-3-1 $$ \left[ \begin{array}{ c c c } c_2 & s_2 c_1 s_2 & s_2 s_1 \\ -s_2 c_3 & s_3 s_1 + c_2 c_3 c_1 & c_2 c_3 s_1 + s_3 c_1 \\ s_2 s_3 & -c2 s_3 c_1 - c_3 s_1 & c_3 c_1 - c_2 s_3 s_1 \end{array} \right] $$ 2-1-2 $$ \left[ \begin{array}{ c c c } c_3 c_1 - c_2 s_3 s_1 & s_2 s_3 & -c_2 s_3 c_1 - c_3 s_1 \\ s_2 s_1 & c_2 & s_2 c_1 \\ c_2 c_3 s_1 + s_3 c_1 & -s_2 c_3 & -s_3 s_1 + c_2 c_3 c_1 \end{array} \right] $$ 2-3-1 $$ \left[ \begin{array}{ c c c } c_2 c_1 & s_2 & -c_2 s_1 \\ s_3 s_1 - s_2 c_3 c_1 & c_2 c_3 & s_3 c_1 + s_2 c_3 s_1 \\ c_3 s_1 + s_2 s_3 c_1 & -c_2 s_3 & c_3 c_1 - s_2 s_3 s_1 \end{array} \right] $$ 3-1-2 $$ \left[ \begin{array}{ c c c } c_3 c_1 - s_2 s_3 s_1 & c_3 s_1 + s_2 s_3 c_1 & -c_2 s_3 \\ -c_2 s_1 & c_2 c_1 & s_2 \\ s_3 c_1 + s_2 c_3 s_1 & s_3 s_1 - s_2 c_3 c_1 & c_2 c_3 \end{array} \right] $$ 1-2-1 $$ \left[ \begin{array}{ c c c } c_2 & s_2 s_1 & -s_2 c_1 \\ s_2 s_3 & c_3 c_1 - c_2 s_3 s_1 & c_3 s_1 + c_2 s_3 c_1 \\ s_2 c_3 & -s_3 c_1 - c_2 c_3 s_1 & -s_3 s_1 + c_2 c_3 c_1 \end{array} \right] $$ 1-3-2 $$ \left[ \begin{array}{ c c c } c_2 c_3 & s_2 c_3 c_1 + s_3 s_1 & s_2 c_3 s_1 - s_3 c_1 \\ -s_2 & c_2 c_1 & c_2 s_1 \\ c_2 s_3 & s_2 s_3 c_1 - c_3 s_1 & s_2 s_3 s_1 + c_3 c_1 \end{array} \right] $$