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Nonlinear computers are capable of simulating nonlinear systems and solving 38 I I . MATHEMATICAL TECHNIQUES FOR LINEAR DIFFERENTIAL EQUATIONS their nonlinear equations. These computers are, in a sense, more important, since they solve problems that usually cannot be solved analytically. We shall merely introduce the use of linear analog computers. Analog computers are very often used as simulators to represent elements of a system. Often the control response and stability of a whole system are to be predicted by testing it, and the computer may substitute for one or more blocks which it may not be feasible to incorporate directly.
Summation and Integration The heart of the modern electronic analog computer is the operational amplifier. It is used in linear computers to integrate and to sum. In diagrams it is represented by the symbol > . Input (error) >\ ^ Output The analyst needs to know only a few things about these amplifiers. One is that they draw practically no error current; another, that their voltage gain is very large, in fact almost infinity; and that their dynamic response is essentially perfect to frequencies higher than those in his problem.
For a given airplane and altitude, CL ~ l/V2, and control deflection versus speed would be like Fig. 3. T h e variation of δ vs V is one of the ways a pilot can recognize stability of the aircraft. It turns out that if the airplane is stable, then starting from any flight condition with its control position, another flight condition at higher speed requires more forward control; and one at lower 54 III. INTRODUCTION TO LONGITUDINAL STABILITY speed requires more aft control. The forces required to hold these stick positions are readily felt, and pilots are used to this relationship between control position, force, and speed.