Appendix/Mathematics/EulerAngles

Euler Angles

$\left[\begin{array}{c}x\\ y\\ z\end{array}\right]$

$Z_1{X}_2{Z}_3$

$=$

$\left[\begin{array}{c}(c_1{c}_3-c_2{s}_1{s}_3)(-c_1{s}_3-c_2{C}_3{s}_1)(s_1{s}_2)\\ (c_3{s}_1+c_1{c}_2{s}_3)(c_1{c}_2{c}_3-s_1{s}_3)(-c_1{s}_2)\\ (s_2{s}_3)(c_3{s}_2)(c_2)\end{array}\right]$

See Also

• Wikipedia Chapter on Euler Angles
• Online class notes from Professor Mona Berciu, Department of Physics & Astronomy, University of British Columbia