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Chapter 7 / Missile Trajectory Optimisation
_ _
Lateral lift force variation due to pitch incidence,
∂ F
∂ Θ
∂ F
∂ Θ
YB
L
MV
B
ZB
L
MV
B
: =
: =
mm
⋅ P&
o
− YB
T
I
mm
⋅ P&
o
− ZB
T
I
, m
, m
⎛
⋅ ⎜
⎝
⎛
⋅ ⎜
⎝
7-10
T
T
MV
B
MV
B
( 6 )
( 9 )
Lateral lift force variation due to yaw incidence,
∂ F
∂ Ψ
YB
L
MV
B
7.3 Missile Controls
: =
m
⋅ P
m o,
m
YB
TI
⎛
⋅ ⎜
⎝
T
MV
B
( 1 )
+
+
−
T
T
T
( 4 )
MV
B
YB
TI
( 7 )
MV
B
ZB
TI
( 4 )
MV
B
YB
TI
∂ TI
⋅
∂ Θ
YB
MV
B
⎞
⎟
⎠
Equation 7.2-39
∂ TI
⋅
∂ Θ
ZB
MV
B
⎞
⎟
⎠
Equation 7.2-40
∂ TI
⋅
∂ Ψ
YB
MV
B
ZB
ZB
YB 2 ∂ FL
MV ∂ TI
( TI
) ⋅ : = − mm
⋅ Po,
m ⋅ TB
( 7 ) ⋅
MV
MV
∂ Ψ
B
⎞
⎟
⎠
Equation 7.2-41
∂ Ψ
B
Equation 7.2-42
The trajectory is optimised by adjusting a set of admissible controls
comprising pitch and yaw incidences, launcher angles, and impact time,
( U M U U )
U ≡
M
C
L
T
Equation 7.3-1
MV MV B
B
( Θ , Ψ M Θ ( 0 ) , Ψ ( 0 ) t )
U : =
M
B
B
A
A
F
Equation 7.3-2
The number of controls must be large enough to accommodate Euler
integration and still approach the optimal solution commensurate with realtime
operation. Using (N := 100) controls to partition the boost and coast
phases,
N
: =
N
B
+ N
C
: =
t B +
0.
1
100 − N
t − t
F
B
B
Equation 7.3-3
It is important that a boundary between controls coincides with the nominal
boost time (tB). As the autopilot uses the coast phase controls the remainder