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            - ;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
                                           8hi - Rt x 8m V:                               (4.301)
                    N
w ere Vi = Ri - (Ro + rb).
Now,
d(8ht) = Ri x 8m V: + Ri x 8m Vi                   (4.302)
 dt
- Rt x 8m Vt
- Ri x 8F,
                                               -. 8Gr
Summing over the entire body, we obtain
                               Gi = E8Gt
                                         = ER: x 8F,
                                         = E ddt (8h:)
(4.303)
(4.304)
(4,305)
(4.306)
 (4.307) .
(4.308)
EQUATIONS OF MOTION AND ESTIMATION OF STABILITY DERIVATIVES 369
= ddt ~- 8hr                                      (4.309)
     d Hi
= c7t                            (4.310)
where Ht  = E 8hi.Equation (4.310)is a basic relationin mechanics, which states
that the time rate ofchange of angular momentum of a rigid body measured in an
inertial space is equal to the net external moment acting on the body with respect
to the origin of the inertial frame of reference.
   Equation (4.310) can be expressed as
                !  dHi
                                       Gi =                                    (4.311)
                 i- dt .
                                          E Rt x 8Ft = ddt E8ht                            (4.312)
　
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