View source for PlanetPhysics/Axis Angle of Rotation to Direction Cosine Matrix

For now, without proof you can get the [[../DirectionCosineMatrix/|direction cosine matrix]] (DCM) from the [[../AxisAngleOfRotation/|axis angle of rotation]] by

<blockquote><math>
\left[ \begin{matrix}
A_{11} & A_{12} & A_{13} \\
A_{21} & A_{22} & A_{23} \\
A_{31} & A_{32} & A_{33} \end{matrix} \right] = \left[ \begin{matrix}
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{matrix} \right]
</math></blockquote>

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