Duncombe / Szebehely Methods in Astrodynamics and Celestial Mechanics

A Selection of Technical Papers Based Mainly on the American Institute of Aeronautics and Astronautics and Institute of Navigation Astrodynamics Specialist Conference Held at Monterey, California, September 16-17, 1965
1. Auflage 2014
ISBN: 978-1-4832-7685-4
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band Volume 17, 452 Seiten, Web PDF

Reihe: Progress in Astronautics and Rocketry

Methods in Astrodynamics and Celestial Mechanics is a collection of technical papers presented at the Astrodynamics Specialist Conference held in Monterey, California, on September 16-17, 1965, under the auspices of the American Institute of Aeronautics and Astronautics and Institute of Navigation. The conference provided a forum for tackling some of the most interesting applications of the methods of celestial mechanics to problems of space engineering. Comprised of 19 chapters, this volume first treats the promising area of motion around equilibrium configurations. Following a discussion on limiting orbits at the equilateral centers of libration, the reader is introduced to the asymptotic expansion technique and its application to trajectories. Asymptotic representations for solutions to the differential equations of satellite theory are considered. The last two sections deal with orbit determination and mission analysis and optimization in astrodynamics. Error equations of inertial navigation as applied to orbital determination and guidance are evaluated, along with parameter hunting procedures and nonlinear optimal control problems with control appearing linearly .This book will be useful to practitioners in the fields of aeronautics, astronautics, and astrophysics.

Autoren/Hrsg.

Duncombe, Raynor L.

Szebehely, Victor G.

Inhaltsverzeichnis

1;Front Cover;1
2;Methods in Astrodynamics and Celestial Mechanics;6
3;Copyright Page;7
4;Table of Contents;16
5;The AIAA Astrodynamics Committee 1965;8
6;The Astrodynamics Specialist Conference Committee 1965;10
7;Preface;12
8;PART I: BEHAVIOR OF BODIES NEAR LIBRATION POINTS;18
8.1;CHAPTER 1. THEORY AND APPLICATION OF MOTION AROUND EQUILIBRIUM POSITIONS;20
8.1.1;Abstract;20
8.1.2;1. General Comments on Equilibrium Solutions;21
8.1.3;2. Restricted Problem of Three Bodies;24
8.1.4;3. Equilibrium Configurations and Linearized Solutions of the Restricted Problem of Three Bodies;27
8.1.5;4. Nonlinear Effects;32
8.1.6;5. Other Models;38
8.1.7;6. Applications;42
8.1.8;References;44
8.2;CHAPTER 2. LIMITING ORBITS AT THE EQUILATERAL CENTERS OF LIBRATION;48
8.2.1;References;51
8.3;CHAPTER 3. MOTION IN THE VICINITY OF LIBRATION POINTS OF A GENERALIZED RESTRICTED THREE-BODY MODEL;54
8.3.1;Abstract;54
8.3.2;Introduction;54
8.3.3;The Generalized Restricted Three-Body Model;56
8.3.4;The Artificial Libration Points;59
8.3.5;Possible Regions of Libration Points as Function of the Acceleration Magnitude;64
8.3.6;Nonconstant Radial Acceleration and the Problem of Stability in the Large;65
8.3.7;References;67
8.4;CHAPTER 4. RESONANCES AFFECTING MOTION NEAR THE EARTH-MOON EQUILATERAL LIBRATION POINTS;72
8.4.1;Abstract;72
8.4.2;I. Introduction;72
8.4.3;II. Equations of Motion;74
8.4.4;III. Solution of theLinearized Equations Corresponding to H;76
8.4.5;IV. Gradual Changes in a1, ß1 Due to H;79
8.4.6;V. Internal Resonant Motion;81
8.4.7;VI. Effect of the Sun;86
8.4.8;VII. Validity of Methods Used;87
8.4.9;VIII. Recommendations;88
8.4.10;References;88
8.5;CHAPTER 5. EFFECT OF INITIAL CONFIGURATIONS ON LIBRATION POINT MOTION;92
8.5.1;Abstract;92
8.5.2;Introduction;92
8.5.3;The Very Restricted Four-Body Problem;95
8.5.4;Model Deficiencies;104
8.5.5;Real World;105
8.5.6;Summary and Conclusions;106
8.5.7;References;107
8.6;CHAPTER 6. ANALYTICAL DETERMINATION OF CHARACTERISTIC EXPONENTS;118
8.6.1;Abstract;118
8.6.2;Introduction;118
8.6.3;Equations of Variation;119
8.6.4;Transition Curves;127
8.6.5;Conclusion;129
8.6.6;Acknowledgements;129
8.6.7;References;129
9;PART II: ASYMPTOTIC REPRESENTATIONS OF SPACE VEHICLE TRAJECTORIES;132
9.1;CHAPTER 7. GENERALIZED METHOD OF AVERAGING AND THE VON ZEIPEL METHOD;134
9.1.1;Abstract;134
9.1.2;Introduction;134
9.1.3;Generalized Method of Averaging;137
9.1.4;The von Zeipel Method;143
9.1.5;Derivation by the Generalized Method of Averaging;148
9.1.6;References;154
9.2;CHAPTER 8. TAKE-OFF FROM A CIRCULAR ORBIT BY A SMALL THRUST;156
9.2.1;Abstract;156
9.2.2;Introduction;157
9.2.3;Formulation of the Problem;158
9.2.4;Derivative-Expansion Method;159
9.2.5;PLK Method;162
9.2.6;Conclusion;167
9.2.7;References;168
9.3;CHAPTER 9. MATCHED ASYMPTOTIC EXPANSIONS, PATCHED CONICS, AND THE COMPUTATION OF INTERPLANETARY TRAJECTORIES;176
9.3.1;Abstract;176
9.3.2;Summary;176
9.3.3;Outline of the Method;178
9.3.4;References;194
9.4;CHAPTER 10. A UNIFORMLY VALID ASYMPTOTIC REPRESENTATION OF SATELLITE MOTION AROUND THE SMALLER PRIMARY IN THE RESTRICTED THREE-BODY PROBLEM;200
9.4.1;Abstract;200
9.4.2;I. Introduction, Equations of Motion;200
9.4.3;II. Summary of the Results;203
9.4.4;References;210
9.5;CHAPTER 11. ASYMPTOTIC REPRESENTATIONS FOR SOLUTIONS TO THE DIFFERENTIAL EQUATIONS OF SATELLITE THEORY;216
9.5.1;Abstract;216
9.5.2;Introduction;216
9.5.3;Solutions, Representations, and Approximations;217
9.5.4;Asymptotics;218
9.5.5;Asymptotic Perturbation Theory;220
9.5.6;Summary;222
9.5.7;References;223
10;PART III: ORBIT DETERMINATION AND MISSION ANALYSIS;224
10.1;CHAPTER 12. ERROR EQUATIONS OF INERTIAL NAVIGATION WITH SPECIAL APPLICATION TO ORBITAL DETERMINATION AND GUIDANCE;226
10.1.1;Abstract;226
10.1.2;Introduction;226
10.1.3;Fundamental Equation of Inertial Navigation;228
10.1.4;Error Equations of an Orbital Inertial Navigator;229
10.1.5;Solution of the Platform-Misalignment-Error Equation;234
10.1.6;Solution of the Position Error Equations;236
10.1.7;Conclusion;245
10.1.8;Appendix A. Notation;246
10.1.9;Appendix B. Review of the Equations of Terrestrial Inertial Navigation;250
10.1.10;References;258
10.2;CHAPTER 13. EFFICIENT AMD ACCURATE ORBIT PREDICTION FOR VERY LONG PERIODS OF TIME;264
10.2.1;Abstract;264
10.2.2;Introduction;264
10.2.3;Derivation of Multistep Predictor Formulas;265
10.2.4;Use of Multistep Methods for Orbit Prediction;270
10.2.5;Accuracy of the Single Step Method;274
10.2.6;Computer Program;275
10.2.7;Numerical Results;276
10.2.8;Appendix: Starting the Multistep Integration;277
10.2.9;References;279
10.3;CHAPTER 14. PARAMETER HUNTING PROCEDURES;286
10.3.1;Abstract;286
10.3.2;Introduction;286
10.3.3;Formulation;288
10.3.4;Implementation Techniques;294
10.3.5;Test Results;297
10.3.6;Conclusions;300
10.3.7;Reference;300
10.4;CHAPTER 15. ACCURACY IN THE DETERMINATION OF LUNAR TRANSPONDER LOCATION FROM POSTARRIVAL TRACKING;314
10.4.1;Abstract;314
10.4.2;I. Introduction;315
10.4.3;II. Preliminary Analysis;316
10.4.4;III. Approximate Expressions for Estimate Accuracy;321
10.4.5;IV. Parallax Contribution to Estimate Accuracy;324
10.4.6;V. Numerical Procedure;326
10.4.7;VI. Discussion of Numerical Results;328
10.4.8;VII. Conclusions;330
10.4.9;References;331
10.5;CHAPTER 16. INTERPLANETARY MANEUVERS IN MANNED HELIONAUTICAL MISSIONS;342
10.5.1;Abstract;342
10.5.2;Nomenclature;342
10.5.3;Introduction;345
10.5.4;Perihelion Brake Maneuver;348
10.5.5;Heliocentric Earth Approach Retro (HEAR) Maneuver;352
10.5.6;Effect of Heliocentric Maneuvers on Orbital Departure Weight of Interplanetary Vehicles;353
10.5.7;Summary and Conclusions;358
11;PART IV: OPTIMIZATION IN ASTRODYNAMICS;370
11.1;CHAPTER 17. A GENERAL METHOD FOR SELECTION AND OPTIMIZATION OF TRAJECTORIES;372
11.1.1;Abstract;372
11.1.2;Introduction;373
11.1.3;Summary;373
11.1.4;1. Nomenclature;374
11.1.5;2. Formulation;374
11.1.6;3. Mechanization of the Inhibitor Control;377
11.1.7;4. Constraints;379
11.1.8;5. Scale Matrices;382
11.1.9;6. Barriers;384
11.1.10;7. Termination Procedures;387
11.1.11;8. An Example;387
11.1.12;9. References;390
11.2;CHAPTER 18. APPLICATION OF A FINITE-DIFFERENCE NEWTON-RAPHSON ALGORITHM TO PROBLEMS OF LOW-THRUST TRAJECTORY OPTIMIZATION;394
11.2.1;Abstract;394
11.2.2;Introduction;395
11.2.3;Method of Approach;396
11.2.4;Application;400
11.2.5;Conclusions;406
11.2.6;References;412
11.3;CHAPTER 19. NONLINEAR OPTIMAL CONTROL PROBLEMS WITH CONTROL APPEARING LINEARLY;418
11.3.1;Abstract;418
11.3.2;1. Introduction;419
11.3.3;2. Control Problem Formulation;421
11.3.4;3. Goddard Problem;425
11.3.5;4. Canonical Forms;440
11.3.6;References;447
12;CONTRIBUTORS TO VOLUME 17;452