A quaternion can be easily constructed from an axis $\vect u_v$ and an angle $\alpha $ using
\begin{equation}
\quat {} = \begin{pmatrix}
\cos \left( \tfrac \alpha 2 \right) \\
\sin \left( \tfrac \alpha 2 \right) \vect u_v
\end{pmatrix} = \begin{pmatrix}
\cos \left( \tfrac \alpha 2 \right) \\
\sin \left( \tfrac \alpha 2 \right) u_x \\
\sin \left( \tfrac \alpha 2 \right) u_y \\
\sin \left( \tfrac \alpha 2 \right) u_z
\end{pmatrix}
\end{equation}
\inHfile{FLOAT\_QUAT\_OF\_AXIS\_ANGLE(q, uv, an)}{pprz\_algebra\_float}