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            (4.315)
                                                                -
                                         = Ro x z~8m V: + Ro x E8mv:
                                                          +ddt y-)  b X 8m V:                       (4.316)
We -note that
                         Ro x ~_ 8m Vi = Ro x X) 8m (Ro + 77lb)                             (4.317)
                                               = Ro x >] 8mRo + R,
         N      Rox~8mrb  (4.318)
                                                        -. O
                                                                                        N                                                                                                    (4.3 19)
     The first term on the right-hand side ofEq. (4.318) vanishes because Ro x Ro  = 0
and the second term vanishes because the body is assumed to be rigid. Furthermore,
using Eq. (4.294), we obtain Ro x 8F1 - Ro x 8m V/.
    With these simplifications, Eq. (4.316) reduces to
E7bx8F,=/t~rbx8m.V:    (4.320) ..
Thus, according to Eq. (4.320), the statement Gr.=dllt/dt of Eq. (4.311) is
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)
　
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