曝光臺 注意防騙
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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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