AIrcraft

In this post I will be discussing the coordinate transformations between the inertial frame, the body frame, and the wind (or stability) frame.

Body to Inertial

The conversion from the body frame to the inertial frame is done using the following transformation: \(\vec{v}_i = q_i^b \otimes \vec{v}_b \otimes q_b^i\) whereby $\otimes$ is the quaternion multiplication and $q_b^i = (q_i^b)^{-1}$ is the attitude quaternion that represents the rotation from the inertial frame to the body frame.