Conversion between quaternions and Euler angles: Difference between revisions

Revision as of 09:43, 26 September 2005

Revision as of 09:50, 26 September 2005

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:<math> \mathbf{q} = \begin{bmatrix}

\cos_2cos (\phi /2) \cos_2cos (\theta /2) \cos_2cos (\psi /2) + \sin_2sin (\phi /2) \sin_2sin (\theta /2) \sin_2sin (\psi /2) \\

\sin_2sin (\phi /2) \cos_2cos (\theta /2) \cos_2cos (\psi /2) - \cos_2cos (\phi /2) \sin_2sin (\theta /2) \sin_2sin (\psi /2) \\

\cos_2cos (\phi /2) \sin_2sin (\theta /2) \cos_2cos (\psi /2) + \sin_2sin (\phi /2) \cos_2cos (\theta /2) \sin_2sin (\psi /2) \\

\cos_2cos (\phi /2) \cos_2cos (\theta /2) \sin_2sin (\psi /2) - \sin_2sin (\phi /2) \sin_2sin (\theta /2) \cos_2cos (\psi /2) \\

\end{bmatrix}</math>

For Euler angles we get:

where <math>\cos_2 \alpha \,</math> is a notational shortcut for <math>\cos \frac{\alpha}{2}</math>, and <math>\sin_2 \alpha \,</math> for <math>\sin \frac{\alpha}{2}</math>. And for Euler angles we get:

:<math>\begin{bmatrix}

Line 48:

\begin{bmatrix}

\mbox{arctan} \frac {2(q_0 q_1 + q_2 q_3)} {1 - 2(q_1^2 + q_2^2)} \\

\mbox{arcsin} (2(q_0 q_2 - q_3 q_1)) \\

\mbox{arctan} \frac {2(q_0 q_3 + q_1 q_2)} {1 - 2(q_2^2 + q_3^2)}

\end{bmatrix} </math>