PERFORMANCE, STABILITY, DYNAMICS, AND CONTROL2(122)

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         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
            - ;SmRo
            -   o
                                   N
                                     - m Vo
(4.295)
(4.296)
(4.297)
(4.298)
(4.299)
(4.300)
The second term on the right-hand side of Eq. (4.298) vanishes because we have
assumed the body to be rigid. Furthermore, note that all the time derivates are to
be taken with respect to the inertial frame of reference xiyizi.
        The angular momentum of the particle P  with respect to the inertial space xt ytzt
is given by
　
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