In these problems the airplane is considered to be disturbed from an initially steady flight condition, with the controls locked in position. Thus, c is zero or a known con­stant. The equations are nonlinear and, consequently, extremely difficult to deal with analytically. In many problems of practical importance, it is satisfactory to linearize the equations by dealing only with small perturbations from the reference condition. In that case we obtain a set of homogeneous linear differential equations with con­stant coefficients, a type that is readily solved. Problems of this class are treated in Chap. 6.


The free-control case is of interest primarily only for manually controlled airplanes. In that case, one or more of the primary control systems is presumed to be freed as in “hands off” by the pilot. The variation of the control angles with time, which is of course needed for the aerodynamic force and moment inputs, is then the result of an interaction between the dynamics and aerodynamics of the vehicle and those of the control system itself, which is usually simplified as a system with one degree of free­dom relative to FB. For a derivation of these equations see Etkin (1972, Sec. 11.3). Each such free control adds one dependent variable and one equation to the mathe­matical system.

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