The Small-Disturbance Theory
As remarked in Sec. 4.8, the equations of motion are frequently linearized for use in stability and control analysis. It is assumed that the motion of the airplane consists of small deviations from a reference condition of steady flight. The use of the small-disturbance theory has been found in practice to give good results. It predicts with satisfactory precision the stability of unaccelerated flight, and it can be used, with sufficient accuracy for engineering purposes, for response calculations where the disturbances are not infinitesimal. There are, of course, limitations to the theory. It is not suitable for solutions of problems in which large disturbance angles occur, for example Ф = 77-/2.
The reasons for the success of the method are twofold: (1) In many cases, the major aerodynamic effects are nearly linear functions of the disturbances, and (2) disturbed flight of considerable violence can occur with quite small values of the linear – and angular-velocity disturbances.