PERFORMANCE, STABILITY, DYNAMICS, AND CONTROL2(125)

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  As said before, for problems in aircraft dynamics,it is usual to ignore the rotation
 of the Earth and assume tO{:,b = tO~.b.
    We have
                 Hb = Ert, x 8mrVt                                        (4.325)
                    = E7b x 8m[Ro+~b]                              (4.326)
                           = E-b x bm[(R'o)b +03lb X Ro + Cr}:,b X -'b]         (4.327)
                      = E8m b x (Ro)b +2~8m7b x c:Obb X Ro
                                 + E 8mrb x mbb x rb                                          (4.328)
                                                                       J
                     = E8mrb x COb.b X rb                                  (4.329)
Using the vector cross product rule of Eq. (4.265), we obtain
                                     Hb = 2x~ [col,b(rb . rt ) - rb(o3lb . rb)]8m                     (4.330)
We have
                                             t3lb = lbp + jbq + kbr                               (4.331)
                                                rb : lbXb + jbyb + kbZb                                 (4.332)
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.
　
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