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

Appendix I / Utilities / Axis Transforms
_ _
a,
b
B
A
( ) ( ) 2
YA
YA
4 ∂ P : = 1 P P
P ⋅ ∂ T
−
P
hA
b
hA
b
3
a,
b
B
A
b
22.4-14
b
a,
b
YA
ZA YA
( 7 ) ∂ P : = − P P
P ⋅ ∂ T
⋅
⋅ ∂
T
B
A
b
YA
YA hA 2
( 2 ) ∂ P : = ( P P ) − 1
b
hA 3 B
YA
YA XA
( P ) ⋅ ∂ T ( 5 ) ∂ P : = − P ⋅ P
b
a,
b
A
∂ T
B
A
B
A
b
YA ( 8 ) ∂ P : = 0
b
YA
ZA YA XA
( 3 ) ∂ Pb
: = Pb
⋅ Pb
⋅ Pb
⋅ 1
P ⋅ P ⋅ ∂ T
ϕ
b
b
b
b
b
Equation 22.4-96
Equation 22.4-97
Equation 22.4-98
b
Equation 22.4-99
Equation 22.4-100
Equation 22.4-101
YA
ZA
( ) ⎜
⎛ YA 2
6 ∂ P : = P ⋅ ( P ) ⋅ ϕ − ⎟
⎞
b
b
b
⎝
⎠
hA
B
Pb a,
b A
1
⋅ P ⋅ ∂ T
1
P
a
, b
⋅ ∂
T
B
A
P
P
XA
hA
YA
b b
( 9 ) ∂ Pb
: = − hA
2
b
P
P
Equation 22.4-102
⋅ P
a,
b
Y
b
Equation 22.4-103
Expressing the transform components in terms of the direction cosines,
∂ T
∂ P
B
A
YA
b
⎡ ∂ T4
⎢
XA
⎢ ∂ Pb
⎢
⎢
2
T2
− 1
: = ⎢
hA
⎢ Pb
⎢
⎢
⎢
⎛
− ⋅ ⋅ ⎜
T1
T
T2
T7
+
⎢ ⎜
⎣ ⎝ Pa
, b P
5
hA
b
⎞
⎟
⎠
,
,
,
T
P
7
hA
b
⋅
1 − T
P
a,
b
∂ T
−
∂ P
T4
⋅ T
−
P
( ) ⎥ ⎥⎥⎥⎥⎥⎥⎥⎥⎥
2 2 T5
+ T2
⋅ T9
T + T − 1 ,
2
2
4
2
XA
b
4
,
,
P
a,
b
0
a,
b
Equation 22.4-104
7
⎤
⎦