Abstract
A problem in the optimization of flight paths concerns the modelling of the thrust force direction. This problem is addressed by considering various mathematical modellings of thrust force directions in a unified approach. When modelling the thrust force direction which is basically related to the vehicle attitude as a linear or non-linear function of angle of attack, higher order optimality conditions are generally not met for interior thrust settings. A convexification technique is developed for efficiently computing a solution. There may be interior arcs as the limiting case of chattering arcs which concern both controls thrust setting and angle of attack of the original system. A numerical example of hypersonic range flight is presented.
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Abbreviations
- C D :
-
drag coefficient
- C L :
-
lift coefficient
- D :
-
drag
- g :
-
gravity acceleration
- H :
-
Hamiltonian
- h :
-
altitude
- J :
-
performance criterion
- L :
-
lift
- M :
-
Mach number
- m :
-
mass
- m f :
-
fuel mass consumed
- r e :
-
radius of the Earth
- S :
-
reference area
- S :
-
switching function
- s :
-
range
- T :
-
thrust
- t :
-
time
- t f :
-
final time
- u :
-
control variables vector
- V :
-
speed
- ϰ :
-
state variables vector
- α :
-
angle of attack
- α T :
-
final time
- γ :
-
flight path angle
- δ T :
-
throttle setting
- ε T :
-
thrust inclination angle (relative to α)
- ζ :
-
control variable of modified system
- λ :
-
adjoint variables vector
- ρ :
-
atmopheric density
- σ :
-
specific fuel consumption
- Φ :
-
Mayer form of performance criterion
- ω e :
-
angular velocity of the Earth
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© 1998 Springer Basel AG
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Sachs, G., Mehlhorn, R., Dinkelmann, M. (1998). Efficient Convexification of Flight Path Optimization Problems. In: Schmidt, W.H., Heier, K., Bittner, L., Bulirsch, R. (eds) Variational Calculus, Optimal Control and Applications. International Series of Numerical Mathematics, vol 124. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8802-8_32
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DOI: https://doi.org/10.1007/978-3-0348-8802-8_32
Publisher Name: Birkhäuser, Basel
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