# 12.4.4: Angular kinematic relations

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In what follows the three components of absolute angular velocity of the aircraft are related with the orientation angles of the aircraft with respect to a local horizon reference system:

$\vec{\omega}_I \approx \vec{\omega}_h = \begin{bmatrix} p \\ q \\ r \end{bmatrix} = \dot{\mu} \vec{i}_w + \dot{\gamma} \vec{j}_1 + \dot{\chi} \vec{k}_h.$

Projecting the unit vectors in wind axes using the appropriate transformation matrices:

$p = \dot{\mu} - \dot{\chi} \sin \gamma$

$q = \dot{\gamma} \cos \mu + \dot{\chi} \cos \gamma \sin \mu$

$r = -\dot{\gamma} \sin \mu + \dot{\chi} \cos \gamma \cos \mu$

This page titled 12.4.4: Angular kinematic relations is shared under a CC BY-SA 3.0 license and was authored, remixed, and/or curated by Manuel Soler Arnedo via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.