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

Chapter 7 / Missile Trajectory Optimisation
_ _
• Missile lateral lift force
ZA
MV MV
FL ( Pm
, P&
o,
m , ΘB
, ΨB
)
• Gravitational acceleration
ZA ZA
g ( P )
Defining,
⎛
⎜
⎜
⎜
⎜
⎜
⎜
⎝
⎛
⎜
⎜
⎜
⎜
⎜
⎜
⎝
T
T
T
147 MV 147 MV 369 MV
( ϕ , ϕ , ϕ )
MV
A
MV
A
MV
A
( 1 )
A
( 4 )
( 7 )
⎞
⎟
⎟
⎟
⎟
⎟
⎟
⎠
,
⎛
⎜
⎜
⎜
⎜
⎜
⎜
⎝
7-5
T
T
T
B
MV
B
MV
B
MV
B
m
( 1 )
( 4 )
( 7 )
⎞
⎟
⎟
⎟
⎟
⎟
⎟
⎠
m
,
B
⎛
⎜
⎜
⎜
⎜
⎜
⎜
⎝
T
T
T
MV
B
MV
B
MV
B
≡
( 3 )
( 6 )
⎞
⎟
⎟
⎟
⎟
⎟
⎟
⎠
⎞
( ) ⎟ ⎟⎟⎟⎟⎟⎟
9
The dynamic states evolve according to the vector functional,
X
( ) T
f , f , f , f , f
f : =
Θ Ψ
P
V
M
⎠
Equation 7.2-4
Equation 7.2-5
The missile position with respect to Alignment axes is propagated using,
147
f : = P ⋅ ϕ &
P
o,
m
MV
A
Equation 7.2-6
Transforming the forces acting along the Missile Body axes through the
incidence angles into the Missile Velocity frame, and selecting the missile
velocity along X MV ,
f
MV
m
MV
B
B
m
MV
B
F : = T ⋅ F : = T ⋅ +
V
: =
m
−1
m
⋅
( ) T
XB XB YB ZB
F F , F , F
T
D
L
L
Equation 7.2-7
XB YB ZB 147 MV ZA MV
( ∆F
, F , F ) ⋅ ϕ + g ⋅ T ( 7 )
m
In which the thrust - drag balance is denoted by,
L
XB
m
L
XB
T
∆ F : = F + F
XB
D
When the missile traces a circle in response to lateral acceleration,
B
m
A
Equation 7.2-8
Equation 7.2-9