PlanetPhysics/Axis Angle of Rotation to Quaternions

Quaternions can be defined from the [[../AxisAngleOfRotation/|axis angle of rotation]] by

$\left[\begin{array}{c}{q}_1\\ q_2\\ q_3\\ q_4\end{array}\right]=\left[\begin{array}{c}{e}_{1}sin(\alpha /2)\\ e_{2}sin(\alpha /2)\\ e_{3}sin(\alpha /2)\\ cos(\alpha /2)\end{array}\right]$