...matrixfaq.

Note the bold-italic (vectors) and bold (matrices) notation. The conversion between vector representations, i.e., Euler angles, and matrix representations is done by algorithms from [8].

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...$R$.$

If $\trace {\M R}$ (sum of the diagonal terms) is zero, the above calculation has to be altered: Iff $r_{1,1} > r_{2,2}$ and $r_{1,1} > r_{3,3}$ then,

$$\dot {\V q} = \left( \begin{array}{l} \frac{1}{2} \frac{r_{2,3} - r_{3,2}}{... ... - r_{1,1} + r_{2,2} - r_{3,3}}} [2.5ex] \end{array}\right),$$

otherwise the quaternion $\dot {\V q}$ is calculated as

$$\dot {\V q} = \left( \begin{array}{l} \frac{1}{2} \frac{r_{1,2} - r_{2,1}}{... ...1 - r_{1,1} - r_{2,2} + r_{3,3}} [1.5ex] \end{array}\right).$$

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