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                                Ba = l711( - Cz8e Cmq CI + Cm8e ITIl  + Cm8t Czq Cl)
                                             - Cxu Cz8e /).I  + Cx8e Czu l).l
                           Cct = Cxu (Cz8e Cmq CI  - Cm8etTll  - Cmbt Czq CI)
                                     - Cxh.Czu Cmq Cl + mi Cx& Cm,, + C.r8r Cmu Czq Cl
                                     + Cxq Cl Czu Cm8, - Cxq Cl Cmu Cz8t
                                    Da = CxO(Czu Cm8e - Cmu Czb,)
The transfer function for pitch angle is given by
AO(s)
A7(s~ =
mis - Clu     -(Cxcr + Cxa,C7S)     C18e
   -Czu     (FirllS - CzaCIS ~ Cza,)   Cz8t
   -Cmu        -(Cmacis + Cma,)     Cmb,
Along(S)
Expanding the determinant in the numerator, we obtain
                                     Na = AOS2 + Bos + Co
where
                                 Ao = lT7.1 (tni Cm8, - Cza Cl Cm8e + Cz8e Cmdr CI)
559
(6.118)
(6.119)
(6.120)
(6.121)
(6.122)
(6.123)
(6.124)
(6.125)
Bo = mi (Czat C,na  - Czo Cm8e)  -  Cxu (ITI I Cm8e - Cza Cl Cm8e  + Cz8,Cmci,Cl)
+ Cl Cxd ( - Cz  Cmbe + Cmu Cz8,) + Cx8e Czu Cma CI
+ CX8e Cm mi - Cne Cmu Czaci                                                   (6.126)
                   Ca  = -Cxu (Cz8e Cma, - Cza Cmb,) + Cxli;t(Cmcr Czu  - Cmu Cz.cr)
                         + Cxa ( - Czu Cm8, + Cmu Cz8,)
We have q -. O, A = AO or q(s) = sO(s), A - sAO(s) so that
                                                q(s)       s AO(s)
                             A8e(s) = A8 (s)
(6.127)
(6.128)
I

560            PERFORMANCE, STABILITY, DYNAMfCS, AND CONTROL
  Transfer function for short-period approximation.  Taking the Laplace
transform of Eqs. (6.41) and (6.42), we have
(mis - Cza CIS - Cza)Aa(s) - [s(m} + Czqq) + CzO]AO(s) = Cz8,A5e(S)
           (6.129)
     -(Cmcr + Cm tcis)Aa(s) + (Iy1S2 - Cmqcis)AO(s) = Cm8,A8e(s)     (6.130)
Dividing throughout by A8e(S) and using Cramer's rule, we obtain the transfer
function for angle of attack.
                        CzBe   -[S(ITII + CzqCi)+ Cz011
Act(s) .  Cm8,  s(lyls-CmqCI) "I
A8e = s(ml~zlr)  zr  Srri+~zqci)+Cz0]1
　
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