Optimal Trajectories in Atmospheric Flight

PrefaceAcknowledgementsNomenclatureIntroduction 0.1 Scope 0.2 Plan of the Study ReferencesChapter 1. Optimization Theory 1.1 Necessary Conditions for Extrema 1.2 Solution Subject to Constraints 1.3 Calculus of Variations 1.3.1 Necessary conditions for optimality 1.3.2 Transversality conditions 1.3.3 Canonical equations 1.3.4 First integrals 1.4 Pontryagin Maximum Principle 1.5 Canonical Transformation ReferencesChapter 2. Switching Theory 2.1 Contensou's Domain of Maneuverability 2.2 Optimal Switching 2.3 Junction With Singular Arc 2.4 Linearized Singular Control ReferencesChapter 3. Equations of Motion 3.1 Introduction 3.2 Relative Angular Motion 3.3 Equations for Flight over a Rotating Spherical Earth 3.4 Equations for Flight over a Flat Earth ReferencesChapter 4. Aerodynamic and Propulsive Forces 4.1 The Atmosphere 4.1.1 Temperature 64 4.1.2 Pressure 4.1.3 Density 4.1.4 Viscosity 4.2 Aerodynamic Forces 4.3 The Drag Polar 4.4 Propulsive Force ReferencesChapter 5. General Properties of Optimal Trajectories 5.1 The Optimal Controls 5.2 Integrals of the Motion 5.3 Application to the Case of Flat Earth 5.4 Application to the Case of Spherical Earth ReferencesChapter 6. Flight in a Horizontal Plane 6.1 Dimensionless Equations of Motion 6.2 Minimum Fuel Turn at Constant Altitude 6.2.1 Optimal controls 6.2.2 Optimal turn to a heading 6.2.3 Optimal turn to a line 6.2.4 Optimal turn to a point 6.3 Optimal Coasting Flight 6.3.1 Optimal lift control 6.3.2 Maximum ranges 6.3.3 The footprint 6.3.4 Some optimal maneuvers ReferencesChapter 7. Optimal Coasting Flight 7.1 Dimensionless Equations of Motion 7.2 Optimal Aerodynamic Control 7.3 Optimal Skip Trajectory 7.3.1 Free final heading 7.3.2 Free final flight path angle 7.3.3 Maximum final altitude 7.3.4 Maximum final speed 7.3.5 Maximum final heading 7.3.6 Maneuvers at small angles 7.4 Optimal Maneuvers in the Vertical Plane 7.4.1 Optimal pull-up maneuver 7.4.2 Solution with bounded lift control 7.4.3 Optimal glide for maximum range 7.4.4 Linearized singular lift control for maximum range ReferencesChapter 8. Supersonic Cruise 8.1 Introduction 8.2 Dimensionless Equations of Motion 8.3 Flight Envelope 8.4 General Analysis 8.5 Maximum Range 8.5.1 Exact analysis 8.5.2 Steady-state cruise 8.6 Maximum Endurance 8.7 Supersonic Cruise With Time Constraint 8.8 Optimality of the Solution ReferencesChapter 9. Supersonic Turn 9.1 Introduction 9.2 Flight Envelope 9.3 Minimum Time Turn 9.3.1 Optimal controls 9.3.2 Turn to a heading 9.3.3 Turn to a point 9. 3.4 Turn to a line 9.4 Minimum Radius Turn 9.5 Minimum Fuel Turn 9.5.1 Optimal controls 9.5.2 Turn to a heading 9.5.3 Turn to a line ReferencesChapter 10. Supersonic Maneuvers in a Vertical Plane 10.1 Dimensionless Equations of Motion 10.2 Glide with Maximum Range 10.3 Cruise by Periodic Control 10.4 Minimum-Time Loop Maneuvers 10.5 Other Maneuvers of Fighter Aircraft 10.6 Minimum-Time to Climb ReferencesChapter 11. Energy State Approximation 11.1 Introduction 11.2 Energy-State Approximation 11.2.1 Minimum-time to climb 11.2.2 Minimum-fuel to climb 11.2.3 Maximum range glide 11.2.4 Minimum-fuel with fixed range 11.3 Loop, Immelman and Split-S 11.4 Three-Dimensional Turns ReferencesChapter 12. Modified Chapmans Formulation for Optimal Reentry Trajectories 12.1 Dimensionless Equations of Motion 12.2 Variational Formulation 12.3 Reduction to the Flat Planet Case 12.4 The Vector Integral 12.5 Flight in the Vacuum ReferencesChapter 13. Optimal Planar Reentry Trajectories 13.1 The Variational Equations 13.2 Optimal Pull Up Maneuver 13.3 Geometry of a Skip Trajectory 13.4 Skip Trajectory for Maximum Final Speed 13.5 Skip Trajectory for Maximum Apogee Altitude 13.6 Skip Trajectory for Maximum Apogee Altitude with Prescribed Apogee Speed 13.7 Skip Trajectory for Maximum Apogee Speed with Prescribed Apogee Altitude 13.8 Skip Trajectory for Maximum Range 13.9 Glide with Maximum Range 13.10 The Nonlinear Equation for the Lift Control ReferencesChapter 14. Optimal Glide of Reentry Vehicles 14.1 Maximum Cross Range 14.2 Approximate Solutions for Maximum Cross Range 14.3 The Footprint of Reentry Vehicle 14.4 Some Related Optimal Glide Problems 14.4.1 Trajectory with maximum final speed 14.4.2 Reaching a latitude with maximum final speed 14.4.3 Closest approach to a prescribed position ReferencesChapter 15. Orbital Aerodynamic Maneuvers 15.1 Introduction 15.2 Orbit Modifications 15.2.1 Aerodynamic capture 15.2.2 Change in the apogee 15.2.3 Change in the eccentricity 15.2.4 Change in the perigee 15.2.5 Change in the major axis 15.3 Rotation of Orbital Plane 15.3.1 Orbital maneuver 15.3.2 Aerodynamic maneuver 15.3.3 Combined maneuver ReferencesAuthor IndexSubject Index