PERFORMANCE, STABILITY, DYNAMICS, AND CONTROL2(128)

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         Fyo + AFy = m[Vo + AV + (ro + Ar)(Uo + AU)
                         - (Po + Ap)( Wo + A W)]                                                   (4.365)
        Fzo + AFz = m[Wo + AW + (Po + Ap)(rVo + A'V)
                   - (qo + Aq)(Uo + AU)]                                              (4.366)
Lo + AL - Ix(po + Ap) - Ixz[(Po + Ap)(qo + Aq) + ro + Ar]
        +(Iz -, Iy)(qo + Aq)(ro + Ar)                                              (4.367)
    Mo + AM = Iy(qo + Aq) + (Ix - lz)(ro + Ar)(po + Ap)
                   +Ixz [(Po + Ap)2 _ (ro + Ar)2]                                                   (4.368)
No + AN - Iz(ro + Ar) - lr-z[Po + Ap - (qo + Aq)(ro + Ar)]
         +(Iy - Ix)(Po + Ap)(qo + Aq)                                                (4.369)
We assume that the aircraft is in a steady, unaccelerated fiight before it encounters
a disturbance, i.e., both the net force and net moment on the aircraft are zero.

374              PERFORMANCE, STABILITY, DYNAMICS, AND CONTROL
Furthermore, in the study of airjllane dynamics, it is customar}r to use the sta-
bility axes system. This impkes that in the equilibrium flight condition prior to
encountering the disturbance, the body axes system coincides with the stability
axes system. However, on encountering the disturbance, the body axes system is
displaced, but the orientation of the stability axes system remains ftxed.
   Mhth these assumptions,
                               Uo -0     Vo = Wo = 0                     (4.370)
so that
Po = qo = ro = O                              (4-371)
Fxo = Fyo = Fzo = 0
 Lo - Mo -.No -0
U-Uo+AU   V-AV   W-AW
P = Ap     q = Aq     r - Ar
Fx - AFx     Fy = AFy     Fz = AFz
L -.AL     M - AM     N - AN
(4.372)
(4.373)
(4.374)
(4.375)
(4.376)
(4.377)
AUU <<1
AUV, ' << 1
~UW << 1               (4.378)
                               p << 1     q <<1      r << 1                     (4.379)
    With these assumptions, second-order terms such as AqA W  can be ignored.
Then Eqs. (4.364-4.369) reduce to the following form:
                                        AFx - mAU                              (4.380)
　
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