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370                PERFORMANCE, STABILITY, DYNAMICS, AND CONTROL
                                       Hb = Eri x 8m V:                           (4.322)
 Then Eq. (4.320) can be expressed as
                                    -b = (dd, )t                          (4.323)
 Using the moving axes theorem from Eq. (4.226),
                          (ddH ): = (ddH )b+C-3rlb X Hb                (4.324)
  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)
　
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