曝光臺 注意防騙 網曝天貓店富美金盛家居專營店坑蒙拐騙欺詐消費者

              (4.49)
    Finally, we consider the angular velocity vector 4, which is directed along the
Oxb axis of the  Oxhybzb system (Fig. 4.3) so that
4b =
(4.50)
EQUATIONS OF MOTION AND ESTIMATION OF STABILITY DERIVATIVES 331
The angular velocity vectorin body axes system Oxbybzb is given by
Therefore,
tOl.,b =
[-q-j,]
(4.51)
[p:] =AB [,;.] +A [:;] + ~~]               (4.52)
Substituting for matrices A and B from Eqs. (4.14) and (4.20), we get
                     O
[pc;f  = [j:S4:SSS,::%  jos4
                       -sin 4
 1 O  01
+Ocos~ ,l[;jl+[%j]  (4.53)
   0  -sin~  ims%j '
Simplif)/ing, we obtain
so that
[q-j,] = [:  _SS:.4,
       p = 4 - ~'sin0
q = O cos 4 + ~' sin ~ cos 0
r : jr cos ~ cos0 - 0 sin ~
~~i]
(4.54)
(4.55)
(4.56)
(4.57)
From Eqs. (4.55-4.57), we observe that very-often-used relations such as p = 4,
q = O, and r -. y. are true only when both the pitch angle 0 and bank angle 4 are
close to zero.
Let
    1  0
Lco =  0   cos4
    0 -sm~
(4.58)
  -sin 0
sin CO:s%] U~]
cOs ~ cOs (
1/lOO:s%]
1i'~s2]
[%i]
332              PERFORMANCE, STABILITY, DYNAMICS, AND CONTROL
so that
                                              ~~i] = ,.-' [-qj,]                                  (4.59)
     The transformation matrix Lo  is not an orthogonal matrix because the vectors
lv, O, and 4 are not mutually perpendicular. Hence, the inverse is not equal to the
 transpose. Therefore, we have to compute L~l  in the usual way as follows:
                               ~:l = (A(1,))adj( ~)                      (4.60)
 The determinant A(L) of matrix Lcn is given by
                                               A(L) = COS2 ~ cos O + S1112 ~ COS 0                              (4.61)
                                                            N cos O                                                                       (4.62)
                N
 The adjoint of matrix L~ is given by
                            'cos0   sin0 sin~   cos@ sin
     adj(Lo,)= O cos~cos0 -s,.,'S,]   (4.63)
                 0    sin~     cos4
 so that
　
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