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Chapter 7 / Missile Trajectory Optimisation
_ _
7.2.3 Dynamic Constraint - Control Jacobians
The optimiser state variation with pitch incidence,
T
MV
MV
MV
( 0 M ∂ f ∂ Θ M ∂ f ∂ Θ M ∂ f ∂ )
MV
∂ X ∂ ΘB
: = 3 V B
Θ B
Ψ
f Θ
m
7-8
B
Equation 7.2-24
MV
B MV
T 147 MV B T 369 MV
( ∂ f ∂ Θ ) : = ( ∂ F ∂ Θ ) ⋅ ϕ − ( F ) ⋅
m ⋅
ϕ
V
m ⋅ Po,
m ⋅ Θ
B
m
B
B
m
B
Equation 7.2-25
MV
B MV
T 369 MV B T 147 MV
( ∂ f ∂ Θ ) : = ( ∂ F ∂ Θ ) ⋅ ϕ + ( F ) ⋅
m &
ϕ
m
m
⋅ P&
o,
m
∂ f
⋅
∂ Ψ
Θ
MV
B
B
⎛ F
: ⎜
∂
=
⎜
⎝ ∂ Ψ
B
m
MV
B
⎞
⎟
⎠
T
⋅
m
369
ϕ
MV
B
B
− F
XB
D
The optimiser state variation with yaw incidence,
⋅ T
MV
B
B
m
B
Equation 7.2-26
YB MV
( 6 ) + F ⋅ T ( 3 )
L
B
Equation 7.2-27
T
MV
MV
MV
( 0 M ∂ f ∂ Ψ M ∂ f ∂ Ψ M ∂ f ∂ )
MV
∂ X ∂ ΨB
: = 3 V B
Θ B
Ψ
f Ψ
∂ F
∂ Ψ
XB
D
MV
B
m
MV
( ∂ f ∂ Ψ )
B
Equation 7.2-28
B MV
T 147 MV XB MV
YB MV
( ∂ F ∂ Ψ ) ⋅ ϕ − F ⋅ T ( 4 ) + F ⋅ T ( 1 )
m
∂ F
∂ Θ
⋅ T
XB
D
MV
B
MV
B
m
⋅ T
m
B
MV
B
&
m
⋅
B
V
D
B
B
: =
MV
( 9 ) ⋅ ( ∂ f ∂ Θ )
MV
m ⋅ Po,
m ⋅ TA
Ψ
∂ F
YB
T
L MV
B 147 MV
( 7 ) + ⋅ T ( 9 ) − ( F ) ⋅ ϕ
P&
∂ F
YB
∂ Θ
MV
B
B
B
m
MV
( 9 ) ⋅ ( ∂ f ∂ Ψ )
MV
m ⋅ o,
m ⋅ TA
Ψ
L
: =
B
Equation 7.2-29
B
Equation 7.2-30
L MV
XB MV
YB MV
( 7 ) + ⋅ T ( 9 ) − ∆F
⋅ T ( 6 ) + F ⋅ T ( 1 )
∂ Ψ
MV
B
B
m
B
B
: =
L
B
Equation 7.2-31