Thesis - Leigh Moody.pdf - Bad Request - Cranfield University

Appendix C / Axis Transforms
_ _
16.12 Alignment to Missile Body Transformation
The transform from the Alignment frame to the Missile Body frame
(TRATOB) is defined using a quaternion to avoid discontinuities as the
missile pitch angle approaches 90°.
16.13 Alignment to Missile and Target LOS Transformations
The Euler triplet defining the orientation of the Missile LOS frame with
respect to the Alignment frame,
E
M
A
: =
−1
ZA hA
−1
YA XA
( 0 , − tan ( P P ) , tan ( P P ) )
m
16-13
m
m
m
Equation 16.13-1
The transform from the Alignment to the Missile LOS frame (TRATOM) is
obtained by substituting these Euler angles into Equation 16.1-4,
T
M
A
: =
⎡ M
cos ΘA
⋅ cos Ψ
⎢
⎢
⎢
M
− sin ΨA
⎢
⎢
⎢ M
⎣ sin ΘA
⋅ cos Ψ
M
A
M
A
,
,
,
cos Θ
sin Θ
M
A
cos Ψ
M
A
⋅ sin Ψ
M
A
⋅ sin Ψ
M
A
M
A
,
,
,
− sin Θ
0
cos Θ
In terms of Cartesian position with respect to the Alignment frame,
T
M
A
: =
⎡ XA
Pm
⎢
⎢ Po,
m
⎢
⎢ YA
Po,
m ⎢ − hA
⎢ Pm
⎢
⎢ XA
⎢ Pm
⋅ P
−
⎢ hA
⎣ Pm
⋅ Po
ZA
m
, m
,
,
,
P
−
P
P
P
P
XA
o,
m
hA
m
YA
m
hA
m
YA
m
o,
m
P
⋅ P
⋅ P
ZA
m
o,
m
,
,
,
M
A
M
A
⎤
⎥
⎥
⎥
⎥
⎥
⎥
⎦
Equation 16.13-2
P
P
ZA
m
o
P
P
hA
m
o
, m
0
, m
⎤
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎦
Equation 16.13-3
The singularity when the elevation is (±π) must be accounted for. If the
slant range is close to zero, a rare occurrence in this application,
C
u
M
A
P < 5 ⇒ T : =
I
3
Equation 16.13-4