PERFORMANCE, STABILITY, DYNAMICS, AND CONTROL2(123)

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                                           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)
                              ~- (Ro+rb) x 8F, = dd ~-- Ri x 8m Vi                 (4.313)
       Ro x ~: 8F: + ~- rl x 8Fr =  ddt L- (Ro + -o,)  x 8m Vt                  (4.314)
                                d
                                                          = ddt E Ro x 8m V: + ddt ~- }:b X 8m Vi.
　
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