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1 Theory of Maxima and Minima＆THEODORE N．EDELBAUM1

1．1 Necessary Conditions for Maxima or Minima2

1．2 Sufficient Conditions for Maxima or Minima4

1．3 Subsidiary Conditions7

1．4 Application to Integrals12

1．5 Remarks on Practical Application16

1．6 Optimization of Low Thrust Trajectories and Propulsion Systems for a 24-Hour Equatorial Satellite19

References31

2 Direct Methods＆FRANK D．FAULKNER33

2．0 Introduction and Summary33

2．1 A Routine for Determining Some Optimum Trajectories35

2．2 Elementary Graphic Solution52

2．3 Optimum Thrust Programming along a Given Curve59

References65

3 Extremization of Linear Integrals by Green＇s Theorem＆ANGELO MIELE69

3．1 Introduction69

3．2 Linear Problem70

3．3 Linear Isoperimetric Problem76

3．4 Linear Problems in Flight Mechanics77

3．5 Optimum Burning Program for a Short-Range,Nonlifting Missile79

3．6 Optimum Drag Modulation Program for the Re-Entry of a Variable-Geometry Ballistic Missile88

References98

4 The Calculus of Variations in Applied Aerodynamics and Flight Mechanics＆ANGELO MIELE99

4．1 Introduction100

4．2 The Problem of Bolza100

4．3 Transformation of Variational Problems109

4．4 The Calculus of Variations in Applied Aerodynamics112

4．5 Bodies of Revolution Having Minimum Pressure Drag in Newtonian Flow113

4．6 Wings Having Minimum Pressure Drag in Linearized Supersonic Flow120

4．7 The Calculus of Variations in Flight Mechanics126

4．8 Optimum Trajectories for Rocket Flight in a Vacuum127

4．9 Optimum Trajectories for Rocket Flight in a Resisting Medium143

4．10 Conclusions163

References163

5 Variational Problems with Bounded Control Variables＆G．LEITMANN171

5．0 Introduction172

5．1 Statement of the Problem172

5．2 Mass Flow Rate Limited Systems174

5．3 Propulsive Power Limited Systems182

5．4 Thrust Acceleration Limited Systems186

5．5 Conclusions192

5．6 Example193

Nomenclature200

Appendix201

References203

6 Methods of Gradients＆HENRY J．KELLEY205

6．0 Introduction206

6．1 Gradient Technique in Ordinary Minimum Problems206

6．2 Gradient Technique in Flight Path Optimization Problems216

6．3 Solar Sailing Example233

6．4 Low-Thrust Example241

6．5 Remarks on the Relative Merits of Various Computational Techniques246

6．6 A Successive Approximation Scheme Employing the Min Operation248

Appendix A251

References252

7 Pontryagin Maximum Principle＆RICHARD E．KOPP255

7．0 Introduction255

7．1 An Introduction to the Pontryagin Maximum Principle256

7．2 The Adjoint System and the Pontryagin Maximum Principle262

7．3 The Calculus of Variations and the Pontryagin Maximum Principle264

7．4 Dynamic Programming and the Pontryagin Maximum Principle271

7．5 Examples274

References278

8 On the Determination of Optimal Trajectories Via Dynamic Programming＆RICHARD BELLMAN281

8．1 Introduction281

8．2 Dynamic Programming282

8．3 One-Dimensional Problems282

8．4 Constraints283

8．5 Constraints—II283

8．6 Discussion284

8．7 Two-Dimensional Problems285

8．8 One-Dimensional Case286

8．9 Discussion288

8．10 Two-Dimensional Case289

8．11 Discussion290

References290

9 Computational Considerations for Some Deterministic and Adaptive Control Processes＆ROBERT KALABA291

9．1 Introduction291

9．2 Some Deterministic Control Processes292

9．3 Adaptive Control Processes305

References308

10 General Imbedding Theory＆C．M．KASHMAR AND E．L．PETERSON311

10．1 Introduction311

10．2 Problem Formulation312

10．3 Elimination of Boundary Valuedness313

10．4 Reduction to Final Value Problem314

10．5 The Classical Solution316

10．6 The Dynamic Programming Solution318

10．7 Summary321

References321

11 Impulsive Transfer between Elliptical Orbits＆DEREK F．LAWDEN323

11．1 Introduction323

11．2 Impulsive Change in Orbital Elements324

11．3 Dependence of Impulse on Orbital Elements328

11．4 Optimal n-Impulse Transfer between Two Terminal Orbits331

11．5 Optimal Two-Impulse Transfer333

11．6 Optimal Slewing of the Orbital Axis334

11．7 Transfer between Orbits Whose Axes Are Aligned341

11．8 Appendix349

References350

12 The Optimum Spacing of Corrective Thrusts in Interplanetary Navigation＆JOHN BREAKWELL353

12．1 Discussion and Results353

12．2 Development of the Optimum Spacing in Example 1363

12．3 Development of the Optimum Spacing in Example 2365

12．4 The Covariance of Dn and Z>n+1 in the Case of Frequent Observations Since Launch;One-Dimensional Model369

12．5 Estimation of D from Frequent Position Measurements since the Last Correction;One-Dimensional Model371

Nomenclature373

General References375

13 Propulsive Efficiency of Rockets＆G．LEITMANN377

13．0 Introduction377

13．1 Propulsive Efficiency—Point Function378

13．2 Propulsive Efficiency—Interval Function381

Nomenclature387

References387

14 Some Topics in Nuclear Rocket Optimization＆R．W．BUSSARD389

14．1 Introduction and Definition389

14．2 High Acceleration Flight396

14．3 Low Acceleration Flight408

14．4 Heat Exchanger Propulsion Systems428

14．5 Nuclear/Electric Propulsion Systems440

References445

AUTHOR INDEX449

SUBJECT INDEX452