PlanetPhysics/Quaternions to Direction Cosine Matrix

Getting the [[../DirectionCosineMatrix/|direction cosine matrix]] (DCM) from quaternions is given in equation 1

$[\begin{matrix} A_{11} & A_{12} & A_{13} \\ A_{21} & A_{22} & A_{23} \\ A_{31} & A_{32} & A_{33} \end{matrix}] = [\begin{matrix} q_{1}^{2} - q_{2}^{2} - q_{3}^{2} + q_{4}^{2} & 2 (q_{1} q_{2} + q_{3} q_{4}) & 2 (q_{1} q_{3} - q_{2} q_{4}) \\ 2 (q_{1} q_{2} - q_{3} q_{4}) & - q_{1}^{2} + q_{2}^{2} - q_{3}^{2} + q_{4}^{2} & 2 (q_{2} q_{3} + q_{1} q_{4}) \\ 2 (q_{1} q_{3} + q_{2} q_{4}) & 2 (q_{2} q_{3} - q_{1} q_{4}) & - q_{1}^{2} - q_{2}^{2} + q_{3}^{2} + q_{4}^{2} \end{matrix}]$

(proof of this conversion to come)

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PlanetPhysics/Quaternions to Direction Cosine Matrix

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