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                         B -  29.3013   2.5764
              O    0
                 -0.2243 -4.6477_
Using MATLAB,I we obtain the eigenvalues ofthe above matrix A as
                                            Ai - 0                                 (6.198)
                                          A2 -. -8.4804                               (6.199)
                                       A3 -. -0.0087                             (6.200)
                           A4.5 = -0.4897+_ j2.3468                   (6.201)
        The dampjng ratio <, natural frequency c.on,period  T, and time for half amplitude
to for the Dutch-roll oscillation are obtained as follows:
                                                <COn : 0.4897                                   (6.202)
            COn    =2.3468       '  (6.203)
              T-- 27r
          co~ 4-2       (6.204)
 a = : 69                                            (6.205)
so that 4' -. 0.2043, tOn - 2.3973 rad/s, T - 2.6773 s, and to -. 1.4090 s-
   The free response of the general aviation airplane to various assumed initial
conditions is shown in Figs. 6.13-6.16. From Fig. 6.13, we observe that the re-
sponse to an initial disturbance in sideslip of Sdeg exhibits osciIJatory motion
due to the Dutch-roll rootrs. The disturbance in sideslip decays to zero witfun
two or three oscillations lasting for about 5 to 6 s. The disturbance in sideslip
570
PERFORMANCE, STABILITY, DYNAMICS, AND CONTROL
Free Lateral-Dlrectional Rasponse of GeneraIAviation Alrplane
Fig. 6.13   Free OongitudinaD response of the general aviation airplane to a distur-
bance in sideslip.
Frea Lataral-Dfrectlonal Response of General Aviation AWdane
Fig 6.14   Free OongitudinaD response of the general arriation airplane to a distur-
 bance in bank angle.
AIRPLANE RESPONSE AND CLOSED-LOOP CONTROL          571
 Free Lateral-Directlonal Response ot General Aviation Airplane
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