It is instructive to investigate the pitching motion caused by a disturbance from trim due to a control surface deflection. We shall assume that the velocity remains constant, and that the only effect of the control input is to cause rotation. In practice, while the primary effect of the elevator deflection will indeed be to create an unbalanced pitching moment that will rapidly generate an angular acceleration, the resulting rotation of the aircraft will lead to changes in the angle of attack, which will cause the lift
and drag forces to change, which in turn will give rise to linear accelerations. These will, however, be lagged with respect to the rotational motion.
We shall assume that the angle of attack (α) and the pitch angle (θ) are the same. We shall neglect downwash lag effects: in other words, the slight time-delay between downwash effects from the main wing reaching the horizontal stabilizer.