Talk:PlanetPhysics/Direction Cosine Matrix to Quaternions

Original TeX Content from PlanetPhysics Archive
%%% This file is part of PlanetPhysics snapshot of 2011-09-01 %%% Primary Title: direction cosine matrix to quaternions %%% Primary Category Code: 45.40.-f %%% Filename: DirectionCosineMatrixToQuaternions.tex %%% Version: 2 %%% Owner: bloftin %%% Author(s): bloftin %%% PlanetPhysics is released under the GNU Free Documentation License. %%% You should have received a file called fdl.txt along with this file. %%% If not, please write to gnu@gnu.org. \documentclass[12pt]{article} \pagestyle{empty} \setlength{\paperwidth}{8.5in} \setlength{\paperheight}{11in}

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The fourth quaternion can be found through the definition given for the axis of rotation (see \htmladdnormallink{axis angle of rotation}{http://planetphysics.org/encyclopedia/AxisAngleOfRotation.html}), $\alpha$

\begin{equation} q_4 = +/- \dfrac{1}{2} \sqrt{A_{11} + A_{22} + A_{33} + 1} \end{equation}

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