Response
Manipulation of the equations of motion yields a second order homogeneous linear differential equation in the angle of attack :
The qualitative behavior of this equation is considered in the article on directional stability. Since and are both negative, the damping is positive. The stiffness does not only depend on the static stability term, it also contains a term which effectively determines the angle of attack due to the body rotation. The distance of the center of lift, including this term, ahead of the centre of gravity is called the maneuver margin. It must be negative for stability.
This damped oscillation in angle of attack and yaw rate, following a disturbance, is called the 'weathercock' mode, after the tendency of a weathercock to point into wind.
Read more about this topic: Stability Derivatives
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