PERFORMANCE, STABILITY, DYNAMICS, AND CONTROL2(126)

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    Returning to moment Eq. (4.324), we have
                          Gb = (dc{l ) +Cr3r~b X Hb
We have
                          (-. )b = bHxb + jb Hyb +kb Hzb
                                                   H.b =  plx - q Iyx - r /xz
                                               Hyb = q Iy - r I),z - plyx
                                                         Hzb = r Iz - p Izx  ~ q Izy
(4.336)
(4.337)
(4.338)
(4.339)
(4.340)
(4.341)
(4.342)
(4.343)
(4.344)
(4.345)
(4.346)
(4.347)
(4.348)
(4.349)

              I

                 i
equivalent to the statement that the sum of all the extemal moments acting on
the body about its mass c. enter (or the or:igin of the body axes system) is equal to
the time rate of change of angular momentum with respect to the inertial system.
Let
                                   Gb = Erb x 8Ft                         (4.321)
372             PERFORMANCE, STABILITY, DYNAMICS, AND CONTROL
and
Wbb X Hb =
   :.
lb
 p
Hxb
 A
Jb
q
Hyb
kb
 r
Hzb
= ib(q Hzb - r Hyt,) +  jb(r Hn - p Hzb)
(4-350)
+ kb(p Hyb - q Hxb)                                       (4.351)
In airplane terminology,
                                         Gb = rTbL + jbM + kbN                            (4.352)
where L is the rolling moment, M is the pitching moment, and N is the yawing
moment. Then substituting and simplifying, we obtain the following equations in
Cartesian form:
                                    L  =  p Ix - q Iyx - r Ixz + q Hzb - r Hyb                               (4.353)
Similarly,
=  p Ix - q Iyx - r Ixz + qr (,tz - Iy) - pq Izx
     + (r2 - q2)lyz + prI).x                                           (4.354)
M = q Iy -r Iyz - plyx + rp(lx - Iz) - qr Ixy
                                      + (P2 _ r2)lzx + pqlzy                                          (4.355)
　
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