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= t,z (Vo)e
(4.285)
                                               = ,  (:V, )e .                              (4.286)
Using the moving axes theorem, we have
                           (ddV, )e = (ddJ, )b+Wl.b X Vo                 (4.287)
    With (Vo)b = lb U + ib V + kb W and 7.o~,b = t70lb = 7b p + 7bq + kbr, we have
                                       (ddV, ), = 7b U + jb V + kb W                          (4.288)
         COe,b X Vo = 7b(q W - Vr) - jb(p W ~ Ur) + kb(p V - Uq)        (4.289)
With
                                               F = Zb Fx + lb Fy + kb Fz                                (4.290)
we have the following force equations for aircraft motion in Cartesian form:
                          Fx =m(U+qW -rV)                  (4.291)
                          Fy -m(V +rU - pW)                  (4.292)
                            Fz -m(W + pV -qU)                    (4.293)
368              PERFORMANCE, STABILITY, DYNAMICS, AND CONTROL
    Theorem on angular momentum.   Consider the motion of a particle P of
mass 8m with respect to the Earth-centered inertial frame ofreference XrYtZt (see
Fig. 4.16). Let XbybZb denote the body-fixed axes system and let the orig:in of the
body-axes system be located at the center of gravity of the body. From Newton's
first law of motion,
8F1 - 8m Vr                                   (4.294)
- 8m Ri
                                                  .= 8m(Ro + rb)
                                                                                                                         . '. -
    Summing over the entire body,
                              Ft = E8F:
                                               = E8m Ro + E 8mrb
　
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