
Optimization Techniques
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Content
- Front Cover
- Optimization Techniques: With Applications to Aerospace Systems
- Copyright Page
- Contents
- Contributors
- Foreword
- Chapter 1. Theory of Maxima and Minima
- 1.1 Necessary Conditions for Maxima or Minima
- 1.2 Sufficient Conditions for Maxima or Minima
- 1.3 Subsidiary Conditions
- 1.4 Application to Integrals
- 1.5 Remarks on Practical Application
- 1.6 Optimization of Low Thrust Trajectories and Propulsion Systems for a 24-Hour Equatorial Satellite
- References
- Chapter 2. Direct Methods
- 2.0 Introduction and Summary
- 2.1 A Routine for Determining Some Optimum Trajectories
- 2.2 Elementary Graphic Solution
- 2.3 Optimum Thrust Programming along a Given Curve
- References
- Chapter 3. Extremization of Linear Integrals by Green's Theorem
- 3.1 Introduction
- 3.2 Linear Problem
- 3.3 Linear Isoperimetric Problem 70
- 3.4 Linear Problems in Flight Mechanics
- 3.5 Optimum Burning Program for a Short-Range, Nonlifting Missile
- 3.6 Optimum Drag Modulation Program for the Re-Entry of a Variable- Geometry Ballistic Missile
- References
- Chapter 4. The Calculus of Variations in Applied Aerodynamics and Flight Mechanics
- 4.1 Introduction
- 4.2 The Problem of Bolza
- 4.3 Transformation of Variational Problems
- 4.4 The Calculus of Variations in Applied Aerodynamics
- 4.5 Bodies of Revolution Having Minimum Pressure Drag in Newtonian Flow
- 4.6 Wings Having Minimum Pressure Drag in Linearized Supersonic Flow
- 4.7 The Calculus of Variations in Flight Mechanics
- 4.8 Optimum Trajectories for Rocket Flight in a Vacuum
- 4.9 Optimum Trajectories for Rocket Flight in a Resisting Medium
- 4.10 Conclusions
- References
- Chapter 5. Variational Problems with Bounded Control Variables
- 5.0 Introduction
- 5.1 Statement of the Problem
- 5.2 Mass Flow Rate Limited Systems
- 5.3 Propulsive Power Limited Systems
- 5.4 Thrust Acceleration Limited Systems
- 5.5 Conclusions
- 5.6 Example
- Nomenclature
- Appendix
- References
- Chapter 6. Methods of Gradients
- 6.0 Introduction
- 6.1 Gradient Technique in Ordinary Minimum Problems
- 6.2 Gradient Technique in Flight Path Optimization Problems
- 6.3 Solar Sailing Example
- 6.4 Low-Thrust Example
- 6.5 Remarks on the Relative Merits of Various Computational Techniques
- 6.6 A Successive Approximation Scheme Employing the Min Operation
- Appendix A
- References
- Chapter 7. Pontryagin Maximum Principle
- 7.0 Introduction
- 7.1 An Introduction to the Pontryagin Maximum Principle
- 7.2 The Adjoint System and the Pontryagin Maximum Principle
- 7.3 The Calculus of Variations and the Pontryagin Maximum Principle
- 7.4 Dynamic Programming and the Pontryagin Maximum Principle
- 7.5 Examples
- References
- Chapter 8. On the Determination of Optimal Trajectories Via Dynamic Programming
- 8.1 Introduction
- 8.2 Dynamic Programming
- 8.3 One-Dimensional Problems
- 8.4 Constraints-I
- 8.5 Constraints-II
- 8.6 Discussion
- 8.7 Two-Dimensional Problems
- 8.8 One-Dimensional Case
- 8.9 Discussion
- 8.10 Two-Dimensional Case
- 8.11 Discussion
- References
- Chapter 9. Computational Considerations for Some Deterministic and Adaptive Control Processes
- 9.1 Introduction
- 9.2 Some Deterministic Control Processes
- 9.3 Adaptive Control Processes
- References
- Chapter 10. General Imbedding Theory
- 10.1 Introduction
- 10.2 Problem Formulation
- 10.3 Elimination of Boundary Valuedness
- 10.4 Reduction to Final Value Problem
- 10.5 The Classical Solution
- 10.6 The Dynamic Programming Solution
- 10.7 Summary
- References
- Chapter 11. Impulsive Transfer between Elliptical Orbits
- 11.1 Introduction
- 11 2 Impulsive Change in Orbital Elements
- 11.3 Dependence of Impulse on Orbital Elements
- 11.4 Optimal n-Impulse Transfer between Two Terminal Orbits
- 11.5 Optimal Two-Impulse Transfer
- 11.6 Optimal Slewing of the Orbital Axis
- 11.7 Transfer between Orbits Whose Axes Are Aligned
- 11.8 Appendix
- References
- Chapter 12. The Optimum Spacing of Corrective Thrusts in Interplanetary Navigation
- 12.1 Discussion and Results
- 12.2 Development of the Optimum Spacing in Example 1
- 12.3 Development of the Optimum Spacing in Example 2
- 12.4 The Covariance of Dn and Dn +1 in the Case of Frequent Observations Since Launch
- One-Dimensional Model
- 12.5 Estimation of D from Frequent Position Measurements since the Last Correction
- One-Dimensional Model
- Nomenclature
- General References
- Chapter 13. Propulsive Efficiency of Rockets
- 13.0 Introduction
- 13.1 Propulsive Efficiency-Point Function
- 13.2 Propulsive Efficiency-Interval Function
- Nomenclature
- References
- Chapter 14. Some Topics in Nuclear Rocket Optimization
- 14.1 Introduction and Definition
- 14.2 High Acceleration Flight
- 14.3 Low Acceleration Flight
- 14.4 Heat Exchanger Propulsion Systems
- 14.5 Nuclear/Electric Propulsion Systems
- References
- Author Index
- Subject Index
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