TABLE OF CONTENTS In this chapter we have studied various axes systems used in airplane dynamics and discussed various methods of transforming vectors from one coordinate system into another. We also studied the methods of calculating time history of Euler angles. The method based on using Euler angle rates has a singularity when the pitch angle approaches 90 deg. However, the direction cosine method and the quaternions do not encounter this problem. We then formulated the problem of airplane dynamics making use of a moving coordinate system to avoid the problem of computing time-varying moments and products of inertia but had to deal with more complex acceleration and angular momentum terms, which render the equations of motion coupled and nonlinear. We then introduced the concept of small disturbances, which enabled us to linearize and decouple the equations of motion into two categories, one set of three equations for longitudinal motion and another set of three equations for lateral-directional motion. The advantage of this approach is that the two motions can be studied independent of each other. We then used Bryan's method and assumed that the aerodynamic forces and moments depend linearly on the instantaneous values of motion variables. We used the method of Taylor series expansion to estimate the aerodynamic forces and moments in the disturbed state. We also discussed engineering methods to evaluate the stability and control derivatives appearing in the Taylor series expansions.
Our next task is to solve the equations of longitudinal and lateral-directional motions to study the...
