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p = Po + Ap q = qo + Aq r - ro + Ar
(4.360)
(4.361)
Fx - F;co + AFx Fy = Fyo + AFy Fz - Fzo + AFz (4.362)
L - Lo+AL M - Mo+AM N - No+AN (4.363)
where the su:ffix o denotes the steady flight condition. Then force Eqs. (4.291-
4.293) and moment Eqs. (4.357-4.359) assume the following form:
Fxo + AFx = m[Uo + AU + (qo + Aq)(Wo + AW) .
- (ro + Ar)( Vo + A V)J (4.364)
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
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