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时间:2010-05-31 02:32来源:蓝天飞行翻译 作者:admin
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-[ie= -sinL cosL _ssl.A,]
               -cos A cos/    -cos A sin /     -
328              PERFORMANCE, STABILITY, DYNAMICS, AND CONTROL
   Inertial system to body axes system    In general, a transformation of this na-
ture will involve all three Euler angles V , O, and 4  Equation (4-22) gives this
transformation matrix T,b as
                     cos8cosqr                      cosOsinp              -sin 6
T/b= sinOsin4cosV,-sinl/cos4 sinysin9sin4+cospcos4 si.,l2:s%]
                     sm0 cos4 cos Vr +sin yr sin 4     sin ~ sin0 cos 4 - cos ~ sin 0     cos 4 co,
              (4.35)
The transformation matrix from body to inertial system is given by
 Tj = (Tib)'
                    coso cos .V     sin0 sin 4 cos ~ -  sin p cos 4     sin 0 cos 4 cos k + sin p su
 _ cosOsinp sinpsinOsin~+cospcos4 sinVsinOcos4-cos,~,,%l
      -sin0       sin4cos0          cos~cos8
              (4.36)
   Wind axes to body axes system.  This transformation involves first rotation
  v : -p, then O  = ct, and finally a rotation 4 of any given value (Fig. 4,6) so that
using Eq. (4.22) we get
         cosacosp          -cosasinp      -sin,
T3= sinctsin4cosp+sinpcos4 -sin)3sinasin4+cospcos4 s,.4':/oo~]
                     sin cr cos 4 cos f/ - sin p sin4     -sin p sin a cos 4 - cos p sin a     cos4 cc
              (4.37)
Thevelocit5rvectormea ssystemisgivenby
             (4.38)
X b( X:,,X
                         
┏━┳━━━━━━━━━┓
┃  ┃~ ~y:             ┃
┃  ┃                . ┃
┗━┻━━━━━━━━━┛
Fiig.4.6   Wind and body axes systems.
yv:) (a)
yw
 ( yb)
EQUATIONS OF MOTION AND ESTIMATION OF STABILITY DERIVATIVES 329
                                 : flight velocity. In the body axes system,

X [U:o]
                 -cos cr sin p
-sin p sina sin~+cos pcos4
-sin  p sin a cos4 - cos p sin a
                              cosa cos p
      - Uo    sina sin4 cos p +sin p cos 4
                     sin cy cos 4 cos p - sin p sin ~
so that
                                                    U - Uo cosa cos p
                                          V  -. Uo (sin a sin 4 cos p + sin p cos ~)
 
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