PlanetPhysics/Axis Angle of Rotation to Quaternions

Quaternions can be defined from the axis angle of rotation by

$[\begin{matrix} q_{1} \\ q_{2} \\ q_{3} \\ q_{4} \end{matrix}] = [\begin{matrix} e_{1} s i n (α / 2) \\ e_{2} s i n (α / 2) \\ e_{3} s i n (α / 2) \\ c o s (α / 2) \end{matrix}]$