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 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)
                                           AFy = m(AV + r Uo)                              (4.381)
AFz = m(A W - qUo)                               (4,382)
AL = plr - rlrz
     AM = q Iy
AN = r Iz - p Ixz
(4.383)
(4.384)
(4.385)
 EQUATIONS OF MOTION AND ESTIMATION OF STABILITY DERIVATIVES 375
Define
 AU
u= U
 AV
v : --
  Uo
 AW
w - -               (4.386)
  Uo
      AFx        AFy        AFz
ACx= pUS' ACy= US  ACz=2pUS  (4.387)
ACi=TAL     AM     AN
  2~pUo2S7 ACrrt=~_pU2S ACn:- JSb (4.388)
                                        :                       = ;-p U2S
so that
  AW
Act ~ ~
   Uo -w
Ap ~ AUV =v
Then, Eqs. (4.380-4.385) take the following form:
                         mUo .
                                           ACx - ~-p U2Su
                                   Z\Cy =   pUU ScAB + r)
      ACz= UUS(Ad-_q)
                          AC,=  p+Sb(PIx -r Ixz)
                         l),
                  ACm= pU S q
                          AC" =  pU~Sb(r Iz - plxz)
(4.389)
(4.390)
(4.391)
(4.392)
(4.393)
(4.394)
(4.395)
(4.396)
(4.397)
(4.398)
         W
　
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