Talk:PlanetPhysics/Axis Angle of Rotation to Direction Cosine Matrix

Original TeX Content from PlanetPhysics Archive
%%% This file is part of PlanetPhysics snapshot of 2011-09-01 %%% Primary Title: axis angle of rotation to direction cosine matrix %%% Primary Category Code: 45.40.-f %%% Filename: AxisAngleOfRotationToDirectionCosineMatrix.tex %%% Version: 4 %%% 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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For now, without proof you can get the \htmladdnormallink{direction cosine matrix}{http://planetphysics.us/encyclopedia/DirectionCosineMatrix.html} (DCM) from the \htmladdnormallink{axis angle of rotation}{http://planetphysics.us/encyclopedia/AxisAngleOfRotation.html} by

\begin{equation} \left[ \begin{array}{ccc} A_{11} & A_{12} & A_{13} \\ A_{21} & A_{22} & A_{23} \\ A_{31} & A_{32} & A_{33} \end{array} \right] = \left[ \begin{array}{ccc} cos(\alpha) + e_1^2(1 - cos(\alpha)) & e_1 e_2 (1 - cos(\alpha)) + e_3 sin(\alpha) & e_1 e_3(1 - cos(\alpha)) - e_2 sin(\alpha) \\ e_1 e_2(1 - cos(\alpha)) - e_3 sin(\alpha) & cos(\alpha) + e_2^2(1 - cos(\alpha)) & e_2 e_3(1-cos(\alpha)) + e_1 sin(\alpha) \\ e_1 e_3(1 - cos(\alpha)) + e_2 sin(\alpha) & e_2 e_3(1-cos(\alpha)) - e_1 sin(\alpha) & cos(\alpha) + e_3^2(1 - cos(\alpha)) \end{array} \right] \end{equation}

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