12.4.4: Angular kinematic relations
- Page ID
- 78417
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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:
\[p = \dot{\mu} - \dot{\chi} \sin \gamma\]
\[q = \dot{\gamma} \cos \mu + \dot{\chi} \cos \gamma \sin \mu\]
\[r = -\dot{\gamma} \sin \mu + \dot{\chi} \cos \gamma \cos \mu\]