Alternative text: $ X = \left( \begin{array}{ccc} 1 & 0 & 0 \\ 0 & cos \phi & -sin \phi \\ 0 & sin \phi & cos \phi \\ \end{array} \right) $
Alternative text: $ Y = \left( \begin{array}{ccc} cos \theta & 0 & sin \theta \\ 0 & 1 & 0 \\ -sin \theta & 0 & cos \theta \\ \end{array} \right) $
Alternative text: $ Z = \left( \begin{array}{ccc} cos \psi & -sin \psi & 0 \\ sin \psi & cos \psi & 0 \\ 0 & 0 & 1 \\ \end{array} \right) $
Alternative text: $ M = Z * Y * Z $
Alternative text: M=\left( \begin{array}{ccc} 1 & 0 & 0 \\ 0 & cos \phi & -sin \phi \\ 0 & sin \phi & cos \phi \\ \end{array} \right)\left( \begin{array}{ccc} cos \theta & 0 & sin \theta \\ 0 & 1 & 0 \\ -sin \theta & 0 & cos \theta \\ \end{array} \right) \left( \begin{array}{ccc} cos \psi & -sin \psi & 0 \\ sin \psi & cos \psi & 0 \\ 0 & 0 & 1 \\ \end{array} \right)$
Alternative text: M=\left( \begin{array}{ccc} 1 & 0 & 0 \\ 0 & cos \phi & -sin \phi \\ 0 & sin \phi & cos \phi \\ \end{array} \right)\left( \begin{array}{ccc} cos \theta cos \psi & -cos \theta sin \psi & sin \theta \\ sin \psi & cos \psi & 0 \\ -sin \theta cos \psi & sin \theta sin \psi & cos \theta \\ \end{array} \right) $
Alternative text: M=\left( \begin{array}{ccc} cos \theta cos \psi & -cos \theta sin \psi & sin \theta \\ cos \phi sin \psi + sin \phi sin \theta cos \psi & cos \phi cos \psi - sin \phi sin \theta sin \psi & -sin \phi cos \theta \\ sin \phi sin \psi - cos \phi sin \theta cos \psi & sin \phi cos \psi + cos \phi sin \theta sin \psi & cos \phi cos \theta \\ \end{array} \right)$
Alternative text: \begin{alignat*}{3} \phi &= atan(\frac{sin \phi}{cos \phi}) &&= atan(\frac{-M_{c2,r1}}{M_{c2,r2}}) \\ \theta &= asin(sin \theta) &&= asin(M_{c2,r0}) \\ \psi &= atan(\frac{sin \psi}{cos \psi}) &&= atan(\frac{-M_{c1,r0}}{M_{c0,r0}}) \\ \end{alignat*}
Alternative text: \begin{flalign*} sin \theta &= 1 \\ cos \theta &= 0 \\ \end{flalign*}
Alternative text: M=\left( \begin{array}{ccc} 0 & 0 & 1 \\ cos \phi sin \psi + sin \phi cos \psi & cos \phi cos \psi - sin \phi sin \psi & 0 \\ sin \phi sin \psi - cos \phi cos \psi & sin \phi cos \psi + cos \phi sin \psi & 0 \\ \end{array} \right)$
Alternative text: \begin{flalign*} sin (\psi + \phi) &= cos \phi sin \psi + sin \phi cos \psi \\ cos (\psi + \phi) &= cos \phi cos \psi - sin \phi sin \psi \\ \end{flalign*}
Alternative text: M=\left( \begin{array}{ccc} 0 & 0 & 1 \\ sin(\psi + \phi) & cos(\psi + \phi) & 0 \\ -cos(\psi + \phi) & sin(\psi + \phi) & 0 \\ \end{array} \right)$
Alternative text: \begin{alignat*}{3} \phi &= 0 &&= 0 \\ \theta &= asin(1) &&= \frac{\pi}{2} \\ \psi &= atan(\frac{sin \psi}{cos \psi}) &&= atan(\frac{M_{c0,r1}}{M_{c1,r1}}) \\ \end{alignat*}
Alternative text: \begin{flalign*} sin \theta &= -1 \\ cos \theta &= 0 \\ \end{flalign*}
Alternative text: M=\left( \begin{array}{ccc} 0 & 0 & -1 \\ cos \phi sin \psi - sin \phi cos \psi & cos \phi cos \psi + sin \phi sin \psi & 0 \\ sin \phi sin \psi + cos \phi cos \psi & sin \phi cos \psi - cos \phi sin \psi & 0 \\ \end{array} \right)$
Alternative text: \begin{flalign*} sin (\psi - \phi) &= cos \phi sin \psi - sin \phi cos \psi \\ cos (\psi - \phi) &= cos \phi cos \psi + sin \phi sin \psi \\ \end{flalign*}
Alternative text: M=\left( \begin{array}{ccc} 0 & 0 & -1 \\ sin(\psi - \phi) & cos(\psi - \phi) & 0 \\ cos(\psi - \phi) & -sin(\psi - \phi) & 0 \\ \end{array} \right)$
Alternative text: \begin{alignat*}{3} \phi &= 0 &&= 0 \\ \theta &= asin(1) &&= \frac{\pi}{2} \\ \psi &= atan(\frac{sin \psi}{cos \psi}) &&= atan(\frac{M_{c0,r1}}{M_{c1,r1}}) \\ \end{alignat*}
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