You just saw the six equations of motion for force-free longitudinal motion. Which three of these equations will change when we incorporate forces and moments?
Remember: forces influence translational and rotational accelerations.
Check the correct three equations.
\dot{x}_I = u \cos \theta + w \sin \theta
\dot{z}_I = -u \sin \theta + w \cos \theta
\dot{\theta} = q
\dot{u} = - qw
\dot{w} = qu
\dot{q} = 0
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