TABLE OF CONTENTS In Chapter 4, we studied various coordinate systems used in airplane dynamics and derived equations of motion applicable for small disturbances. We also discussed the methods of evaluating various stability and control derivatives appearing in those equations. Under the assumption of small disturbance, the equations of motion could be grouped into two sets of three equations each: one set for longitudinal motion and another set for lateral-directional motion of the aircraft. This kind of decoupling enables us to study separately the longitudinal and lateral-directional response and closed-loop control. In Chapter 5, we studied the basic principles of linear system theory and design of closed-loop control systems.
In this chapter we will discuss the solution of the small-disturbance equations to determine the airplane response. The airplane response depends on the initial conditions and the input time history. The response to a given set of initial conditions with zero input is called the natural or free response. The free response is indicative of the transient behavior or the dynamic stability of the system. The initial conditions are equivalent to suddenly imposed disturbances. For example, the response with u(0) = 0, ? ?(0) = 5 deg, and q = ? ? = 0 is equivalent to the response for a suddenly imposed vertical gust that momentarily increases the airplane angle of attack by 5 deg.
The forced response is the solution of equations of motion with zero initial conditions and a given input time history. The forced...
