axis angle of rotation to quaternionsAxisAngleOfRotationToQuaternions2005-08-28 23:44:022005-08-29 00:24:32Definition% this is the default PlanetMath preamble. as your knowledge
% of TeX increases, you will probably want to edit this, but
% it should be fine as is for beginners.
% almost certainly you want these
\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{amsfonts}
% used for TeXing text within eps files
%\usepackage{psfrag}
% need this for including graphics (\includegraphics)
%\usepackage{graphicx}
% for neatly defining theorems and propositions
%\usepackage{amsthm}
% making logically defined graphics
%\usepackage{xypic}
% there are many more packages, add them here as you need them
% define commands hereQuaternions can be defined from the axis angle of rotation by
\begin{equation}
\left[ \begin{array}{c}
q_1 \\
q_2 \\
q_3 \\
q_4 \end{array} \right] =
\left[ \begin{array}{c}
e_1 sin( \alpha /2 ) \\
e_2 sin( \alpha /2 ) \\
e_3 sin( \alpha /2 ) \\
cos( \alpha /2 ) \end{array} \right]
\end{equation}