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

Appendix I / Utilities / Axis Transforms
_ _
E
B
A
: =
−1
ZA hA
−1
YA XA
( 0 , − tan ( P P ) , tan ( P P ) )
b
22.4-2
b
b
b
Equation 22.4-5
XA
YA
ZA
B
( P b < ∆ ) ∧ ( Pb
< ∆ ) ∧ ( Pb
< ∆ ) ⇒ EA
: = 03
XA
YA
ZA
( ( P < ∆ ) ∧ ( P < ∆ ) ) ∧ ( P ≥ ∆ )
b
E
B
A
: =
b
( 0 , − π 2 , 0 )
b
Equation 22.4-6
⇒
Equation 22.4-7
E_ANGLES determines the orientation of frame (B) from the linear velocity
and acceleration of point (b) expressed in ENU geodetic axes (A) assuming
zero incidence and a non-zero roll angle,
E_ANGLES
A A ZA B
E A A ZA
( A , V , g , E ) ≡ ϕ ( A , V , g )
b
b
b
A
LD
b
b
b
Equation 22.4-8
The linear velocity and acceleration of point (b) with respect to point (a),
and the local gravitational acceleration at (b), determine the Euler triplet,
E
B
A
C
b
: =
B
−1
ZA hA
−1
YA XA
( Φ , − tan ( V V ) , tan ( V V ) )
A
C
A
b
b
b
b
Equation 22.4-9
( ) ( ) T
B B XA YA ZA ZA
0 Θ Ψ ⋅ A , A , A g
A : = T
+
A
A
b
b
b
b
Equation 22.4-10
YC
ZC
B
−1
YC ZC
( A > ∆ ) ∨ ( A > ∆ ) ⇒ Φ : = − tan ( A A )
b
b
YC
ZC
B
( A ≤ ∆ ) ∧ ( A ≤ ∆ ) ⇒ Φ : = 0
b
A
A
YB
b
YB
b
≥
<
0
0
⇒
⇒
b
Φ
Φ
B
A
B
A
A
: =
: =
Φ
Φ
B
A
B
A
A
+ π
− π
b
Equation 22.4-11
Equation 22.4-12
Equation 22.4-13
Equation 22.4-14
b