动力机械和机身手册2(93)

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Here, Xb, yb, Zb are the coordinates of the particle P of mass 8m in the body axes
EQUATIONS OF MOTION AND ESTIMATION OF STABILITY DERIVATIVES 371
system. Assuming Hb = 7bllxb +  jbllyb + kbHzb, Eq. (4.330) can be expressed
in Cartesian form as
where
Hxb = ~ p8m(xb2 + yb2 + z~) - X~) 8tTi(pxb2 + qxbyb + rxt,zb)   (4.333)
Hyb = Eq8mcxb2 + yb2 + z~) - y- 8m(pxt,Yt + qyb2 + rybzb)   (4.334)
Hzh = ~- r8m(xt2 + yb2 + z~) - ~~ 8m(pxbzb + qybzb + rz~)   (4.335)
Hxb = pIx - q Ixy - r Ixz
Hyb = qIy - r /yz - plyx
Hzb = r /z - pIzx - q/zy
Ix = lv/j: 8m(yb2 + z~)
Iy  = E 8tri (Xb2 + zg)
Iz = 1- 8m (x~ + y~)
   Ixy = X: 8mxbyb
  Iyz = E8mybzb
                                  Iu = ~18mxbzb
 Note that In, = Iyx, Izx = Ixz, and Iyz = Izy.
    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)
　
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