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

Appendix I / Utilities / Point Mass Kinematics
_ _
DE_TO_W
ω
B
A,
B
: =
If the roll angle is zero,
ω
B
A,
B
B B B
W B B
( E&
, E , ω ) ≡ ϕ ( E&
, E )
⎛
⎜
⎜
⎜
⎜
⎜
⎜
⎝
Ψ&
Ψ&
A
B
A
B
A
22.5.6 Angular to Euler (YPR) Rates
A
⋅ sin Φ
⋅ cosΦ
22.5-5
Φ&
B
A
B
A
B
A
A,
B
− Ψ&
B
A
⋅ cosΘ
⋅ cosΘ
⋅ sin Θ
B
A
B
A
+ Θ&
DE
B
A
− Θ&
B
A
B
A
A
⋅ cosΦ
⋅ sin Φ
A
Equation 22.5-25
B
A
B
A
⎞
⎟
⎟
⎟
⎟
⎟
⎟
⎠
( ) T
B B B B B
− Ψ&
⋅ sin Θ , Θ&
, Ψ&
⋅ cos
: =
Θ
A
A
A
A
Equation 22.5-26
A
Equation 22.5-27
W_TO_DE takes the angular rate of frame (B) with respect to frame (A),
and Euler triplet representing the orientation between the two, and returns
the Euler rate of frame (B) with respect to frame (A).
W_TO_DE
E&
B
A
: =
⎛
⎜
⎜
⎜
⎜
⎜
⎜
⎝
If the roll angle is zero,
B
A
B B B
DE B B
( ω , E , E&
) ≡ ϕ ( ω , E )
A,
B
A
YB B ZB B
( ω ⋅ sin Φ + ω ⋅ cosΦ
)
A,
B
ω
YB
A,
B
ω
XB
A,
B
A
A
⋅ cosΦ
+ Ψ&
B
A
B
A
− ω
A,
B
ZB
A,
B
W
⋅ sin Θ
B
A
⋅ sin Φ
A
A,
B
B
A
⋅ secΘ
A
Equation 22.5-28
B
A
⎞
⎟
⎟
⎟
⎟
⎟
⎟
⎠
ZB B YB ZB B
( ω ⋅ tan Θ , ω , ω ⋅ sec )
E& : =
Θ
A,
B
22.5.7 Euler to Angular Accelerations
A
A,
B
A,
B
T
Equation 22.5-29
A
Equation 22.5-30
D2E_TO_DW takes an Euler triplet representing the orientation of frame (B)
with respect to frame (A), and its Euler rate and acceleration, and returns the
angular acceleration.