Methods of celestial mechanics: 1 Physical, mathematical, and numerical principles
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2005
|
| Schriftenreihe: | Astronomy and astrophysics library
|
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVI, 464 S. 1 CD-ROM (12 cm) |
| ISBN: | 3540407499 |
Internformat
MARC
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| 100 | 1 | |a Beutler, Gerhard |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Methods of celestial mechanics |n 1 |p Physical, mathematical, and numerical principles |c Gerhard Beutler |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2005 | |
| 300 | |a XVI, 464 S. |e 1 CD-ROM (12 cm) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Astronomy and astrophysics library | |
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Datensatz im Suchindex
| _version_ | 1804135022779695104 |
|---|---|
| adam_text | Contents
Part I. Physical, Mathematical, and Numerical Principles
1. Overview of the Work 3
1.1 Part I: Theory 3
1.2 Part II: Applications 9
1.3 Part III: Program System 14
2. Historical Background 19
2.1 Milestones in the History of Celestial Mechanics
of the Planetary System 19
2.2 The Advent of Space Geodesy 31
3. The Equations of Motion 45
3.1 Basic Concepts 46
3.2 The Planetary System 50
3.2.1 Equations of Motion of the Planetary System 51
3.2.2 First Integrals 55
3.3 The Earth Moon Sun System 61
3.3.1 Introduction 61
3.3.2 Kinematics of Rigid Bodies 63
3.3.3 The Equations of Motion in the Inertial System 71
3.3.4 The Equations of Motion in the Body Fixed Systems . 78
3.3.5 Development of the Equations of Motion 80
3.3.6 Second Order Differential Equations
for the Euler Angles $ , e and O 90
3.3.7 Kinematics of the Non Rigid Earth 91
3.3.8 Liouville Euler Equations of Earth Rotation 94
3.4 Equations of Motion for an Artificial Earth Satellite 96
3.4.1 Introduction 96
3.4.2 Equations for the Center of Mass of a Satellite 97
3.4.3 Attitude of a Satellite 110
3.5 Relativistic Versions of the Equations of Motion 116
3.6 The Equations of Motion in Overview 120
XII Contents
4. The Two and the Three Body Problems 123
4.1 The Two Body Problem 123
4.1.1 Orbital Plane and Law of Areas 123
4.1.2 Shape and Size of the Orbit 125
4.1.3 The Laplace Integral and the Laplace Vector q 130
4.1.4 True Anomaly uasa Function of Time:
Conventional Approach 132
4.1.5 True Anomaly v as a Function of Time:
Alternative Approaches 137
4.2 State Vector and Orbital Elements 140
4.2.1 State Vector Orbital Elements 142
4.2.2 Orbital elements — State Vector 143
4.3 Osculating and Mean Elements 144
4.4 The Relativistic Two Body Problem 147
4.5 The Three Body Problem 150
4.5.1 The General Problem 152
4.5.2 The Probleme Restreint 155
5. Variational Equations 175
5.1 Motivation and Overview 175
5.2 Primary and Variational Equations 176
5.3 Variational Equations of the Two Body Problem 183
5.3.1 Elliptic Orbits 186
5.3.2 Parabolic Orbits 190
5.3.3 Hyperbolic Orbits 192
5.3.4 Summary and Examples 193
5.4 Variational Equations Associated with One Trajectory 195
5.5 Variational Equations Associated with the /V Body Problem . 198
5.6 Efficient Solution of the Variational Equations 202
5.6.1 Trajectories of Individual Bodies 203
5.6.2 The iV Body Problem 205
5.7 Variational Equations and Error Propagation 206
6. Theory of Perturbations 209
6.1 Motivation and Classification 209
6.2 Encke Type Equations of Motion 211
6.3 Gaussian Perturbation Equations 215
6.3.1 General Form of the Equations 215
6.3.2 The Equation for the Semi major Axis a 217
6.3.3 The Gaussian Equations in Terms of Vectors h, q .... 218
6.3.4 Gaussian Perturbation Equations in Standard Form . . 223
6.3.5 Decompositions of the Perturbation Term 228
6.4 Lagrange s Planetary Equations 232
6.4.1 General Form of the Equations 232
6.4.2 Lagrange s Equation for the Semi major Axis a 234
Contents XIII
6.4.3 Lagrange s Planetary Equations 234
6.5 First and Higher Order Perturbations 240
6.6 Development of the Perturbation Function 242
6.6.1 General Perturbation Theory
Applied to Planetary Motion 243
6.7 Perturbation Equation for the Mean Anomaly a(t) 247
7. Numerical Solution of Ordinary Differential
Equations: Principles and Concepts 253
7.1 Introduction 253
7.2 Mathematical Structure 255
7.3 Euler s Algorithm 259
7.4 Solution Methods in Overview 264
7.4.1 Collocation Methods 264
7.4.2 Multistep Methods 266
7.4.3 Taylor Series Methods 269
7.4.4 Runge Kutta Methods 271
7.4.5 Extrapolation Methods 275
7.4.6 Comparison of Different Methods 277
7.5 Collocation 279
7.5.1 Solution of the Initial Value Problem 280
7.5.2 The Local Boundary Value Problem 283
7.5.3 Efficient Solution of the Initial Value Problem 285
7.5.4 Integrating a Two Body Orbit
with a High Order Collocation Method: An Example.. 291
7.5.5 Local Error Control with Collocation Algorithms 295
7.5.6 Multistep Methods as Special Collocation Methods . .. 304
7.6 Linear Differential Equation Systems
and Numerical Quadrature 312
7.6.1 Introductory Remarks 312
7.6.2 Taylor Series Solution 313
7.6.3 Collocation for Linear Systems: Basics 315
7.6.4 Collocation: Structure of the Local Error Function .... 317
7.6.5 Collocation Applied to Numerical Quadrature 320
7.6.6 Collocation: Examples 324
7.7 Error Propagation 330
7.7.1 Rounding Errors in Digital Computers 332
7.7.2 Propagation of Rounding Errors 334
7.7.3 Propagation of Approximation Errors 341
7.7.4 A Rule of Thumb for Integrating Orbits
of Small Eccentricities
with Constant Stepsize Methods 348
7.7.5 The General Law of Error Propagation 350
XIV Contents
8. Orbit Determination and Parameter Estimation 355
8.1 Orbit Determination as a Parameter Estimation Problem .... 355
8.2 The Classical Pure Orbit Determination Problem 356
8.2.1 Solution of the Classical Orbit Improvement Problem . 357
8.2.2 Astrometric Positions 363
8.3 First Orbit Determination 366
8.3.1 Determination of a Circular Orbit 369
8.3.2 The Two Body Problem as a Boundary Value Problem 373
8.3.3 Orbit Determination as a Boundary Value Problem . .. 378
8.3.4 Examples 381
8.3.5 Determination of a Parabolic Orbit 384
8.3.6 Gaussian vs. Laplacian Type Orbit Determination . .. 388
8.4 Orbit Improvement: Examples 396
8.5 Parameter Estimation in Satellite Geodesy 404
8.5.1 The General Task 405
8.5.2 Satellite Laser Ranging 406
8.5.3 Scientific Use of the GPS 413
8.5.4 Orbit Determination for Low Earth Orbiters 423
References 441
Abbreviations and Acronyms 449
Name Index 453
Subject Index 455
Contents of Volume II
Part II. Applications
1. Volume II in Overview
1.1 Review of Volume I
1.2 Part II: Applications
1.3 Part III: Program System
2. The Rotation of Earth and Moon
2.1 Basic Facts and Observational Data
2.2 The Rotation of a Rigid Earth and a Rigid Moon
2.3 Rotation of the Non Rigid Earth
2.4 Rotation of Earth and Moon: A Summary
3. Artificial Earth Satellites
3.1 Oblateness Perturbations
3.2 Higher Order Terms of the Earth Potential
3.3 Resonance with Earth Rotation
3.4 Perturbations due to the Earth s Stationary Gravitational Field
in Review
3.5 Non Gravitational Forces
3.6 Atmospheric Drag
3.7 Radiation Pressure
3.8 Comparison of Perturbations Acting on Artificial Earth Satellites
4. Evolution of the Planetary System
4.1 Development of the Outer Planetary System
4.2 Development of the Inner Planetary System
4.3 Minor Planets
XVI Contents of Volume II
Part III. Program System
5. The Program System CelestialMechanics
5.1 Computer Programs
5.2 Menu System
6. The Computer Programs NUMINT and LINEAR
6.1 Program NUMINT
6.2 Program LINEAR
7. The Computer Programs SATORB and LEOKIN
7.1 Program SATORB
7.2 Kinematic LEO Orbits: Program LEOKIN
7.3 Dynamic and Reduced Dynamics LEO Orbits
Using Program SATORB
8. The Computer Program ORBDET
8.1 Introduction
8.2 Orbit Determination as a Boundary Value Problem
8.3 Determination of a Circular Orbit
9. The Computer Program ERDROT
9.1 Earth Rotation
9.2 Rotation of the Moon
9.3 The TV Body Problem Earth Moon Sun Planets
9.4 Space Geodetic and Atmospheric Aspects of Earth Rotation
10. The Computer Program PLASYS
11. Elements of Spectral Analysis
and the Computer Program FOURIER
11.1 Statement of the Problem
11.2 Harmonic Analysis Using Least Squares Techniques
11.3 Classical Discrete Fourier Analysis
11.4 Fast Fourier Analysis
11.5 Prograde and Retrograde Motions of Vectors
11.6 The Computer Program FOURIER
References
Abbreviations and Acronyms
Name Index
Subject Index
|
| adam_txt |
Contents
Part I. Physical, Mathematical, and Numerical Principles
1. Overview of the Work 3
1.1 Part I: Theory 3
1.2 Part II: Applications 9
1.3 Part III: Program System 14
2. Historical Background 19
2.1 Milestones in the History of Celestial Mechanics
of the Planetary System 19
2.2 The Advent of Space Geodesy 31
3. The Equations of Motion 45
3.1 Basic Concepts 46
3.2 The Planetary System 50
3.2.1 Equations of Motion of the Planetary System 51
3.2.2 First Integrals 55
3.3 The Earth Moon Sun System 61
3.3.1 Introduction 61
3.3.2 Kinematics of Rigid Bodies 63
3.3.3 The Equations of Motion in the Inertial System 71
3.3.4 The Equations of Motion in the Body Fixed Systems . 78
3.3.5 Development of the Equations of Motion 80
3.3.6 Second Order Differential Equations
for the Euler Angles $ , e and O 90
3.3.7 Kinematics of the Non Rigid Earth 91
3.3.8 Liouville Euler Equations of Earth Rotation 94
3.4 Equations of Motion for an Artificial Earth Satellite 96
3.4.1 Introduction 96
3.4.2 Equations for the Center of Mass of a Satellite 97
3.4.3 Attitude of a Satellite 110
3.5 Relativistic Versions of the Equations of Motion 116
3.6 The Equations of Motion in Overview 120
XII Contents
4. The Two and the Three Body Problems 123
4.1 The Two Body Problem 123
4.1.1 Orbital Plane and Law of Areas 123
4.1.2 Shape and Size of the Orbit 125
4.1.3 The Laplace Integral and the Laplace Vector q 130
4.1.4 True Anomaly uasa Function of Time:
Conventional Approach 132
4.1.5 True Anomaly v as a Function of Time:
Alternative Approaches 137
4.2 State Vector and Orbital Elements 140
4.2.1 State Vector Orbital Elements 142
4.2.2 Orbital elements — State Vector 143
4.3 Osculating and Mean Elements 144
4.4 The Relativistic Two Body Problem 147
4.5 The Three Body Problem 150
4.5.1 The General Problem 152
4.5.2 The Probleme Restreint 155
5. Variational Equations 175
5.1 Motivation and Overview 175
5.2 Primary and Variational Equations 176
5.3 Variational Equations of the Two Body Problem 183
5.3.1 Elliptic Orbits 186
5.3.2 Parabolic Orbits 190
5.3.3 Hyperbolic Orbits 192
5.3.4 Summary and Examples 193
5.4 Variational Equations Associated with One Trajectory 195
5.5 Variational Equations Associated with the /V Body Problem . 198
5.6 Efficient Solution of the Variational Equations 202
5.6.1 Trajectories of Individual Bodies 203
5.6.2 The iV Body Problem 205
5.7 Variational Equations and Error Propagation 206
6. Theory of Perturbations 209
6.1 Motivation and Classification 209
6.2 Encke Type Equations of Motion 211
6.3 Gaussian Perturbation Equations 215
6.3.1 General Form of the Equations 215
6.3.2 The Equation for the Semi major Axis a 217
6.3.3 The Gaussian Equations in Terms of Vectors h, q . 218
6.3.4 Gaussian Perturbation Equations in Standard Form . . 223
6.3.5 Decompositions of the Perturbation Term 228
6.4 Lagrange's Planetary Equations 232
6.4.1 General Form of the Equations 232
6.4.2 Lagrange's Equation for the Semi major Axis a 234
Contents XIII
6.4.3 Lagrange's Planetary Equations 234
6.5 First and Higher Order Perturbations 240
6.6 Development of the Perturbation Function 242
6.6.1 General Perturbation Theory
Applied to Planetary Motion 243
6.7 Perturbation Equation for the Mean Anomaly a(t) 247
7. Numerical Solution of Ordinary Differential
Equations: Principles and Concepts 253
7.1 Introduction 253
7.2 Mathematical Structure 255
7.3 Euler's Algorithm 259
7.4 Solution Methods in Overview 264
7.4.1 Collocation Methods 264
7.4.2 Multistep Methods 266
7.4.3 Taylor Series Methods 269
7.4.4 Runge Kutta Methods 271
7.4.5 Extrapolation Methods 275
7.4.6 Comparison of Different Methods 277
7.5 Collocation 279
7.5.1 Solution of the Initial Value Problem 280
7.5.2 The Local Boundary Value Problem 283
7.5.3 Efficient Solution of the Initial Value Problem 285
7.5.4 Integrating a Two Body Orbit
with a High Order Collocation Method: An Example. 291
7.5.5 Local Error Control with Collocation Algorithms 295
7.5.6 Multistep Methods as Special Collocation Methods . . 304
7.6 Linear Differential Equation Systems
and Numerical Quadrature 312
7.6.1 Introductory Remarks 312
7.6.2 Taylor Series Solution 313
7.6.3 Collocation for Linear Systems: Basics 315
7.6.4 Collocation: Structure of the Local Error Function . 317
7.6.5 Collocation Applied to Numerical Quadrature 320
7.6.6 Collocation: Examples 324
7.7 Error Propagation 330
7.7.1 Rounding Errors in Digital Computers 332
7.7.2 Propagation of Rounding Errors 334
7.7.3 Propagation of Approximation Errors 341
7.7.4 A Rule of Thumb for Integrating Orbits
of Small Eccentricities
with Constant Stepsize Methods 348
7.7.5 The General Law of Error Propagation 350
XIV Contents
8. Orbit Determination and Parameter Estimation 355
8.1 Orbit Determination as a Parameter Estimation Problem . 355
8.2 The Classical Pure Orbit Determination Problem 356
8.2.1 Solution of the Classical Orbit Improvement Problem . 357
8.2.2 Astrometric Positions 363
8.3 First Orbit Determination 366
8.3.1 Determination of a Circular Orbit 369
8.3.2 The Two Body Problem as a Boundary Value Problem 373
8.3.3 Orbit Determination as a Boundary Value Problem . . 378
8.3.4 Examples 381
8.3.5 Determination of a Parabolic Orbit 384
8.3.6 Gaussian vs. Laplacian Type Orbit Determination . . 388
8.4 Orbit Improvement: Examples 396
8.5 Parameter Estimation in Satellite Geodesy 404
8.5.1 The General Task 405
8.5.2 Satellite Laser Ranging 406
8.5.3 Scientific Use of the GPS 413
8.5.4 Orbit Determination for Low Earth Orbiters 423
References 441
Abbreviations and Acronyms 449
Name Index 453
Subject Index 455
Contents of Volume II
Part II. Applications
1. Volume II in Overview
1.1 Review of Volume I
1.2 Part II: Applications
1.3 Part III: Program System
2. The Rotation of Earth and Moon
2.1 Basic Facts and Observational Data
2.2 The Rotation of a Rigid Earth and a Rigid Moon
2.3 Rotation of the Non Rigid Earth
2.4 Rotation of Earth and Moon: A Summary
3. Artificial Earth Satellites
3.1 Oblateness Perturbations
3.2 Higher Order Terms of the Earth Potential
3.3 Resonance with Earth Rotation
3.4 Perturbations due to the Earth's Stationary Gravitational Field
in Review
3.5 Non Gravitational Forces
3.6 Atmospheric Drag
3.7 Radiation Pressure
3.8 Comparison of Perturbations Acting on Artificial Earth Satellites
4. Evolution of the Planetary System
4.1 Development of the Outer Planetary System
4.2 Development of the Inner Planetary System
4.3 Minor Planets
XVI Contents of Volume II
Part III. Program System
5. The Program System CelestialMechanics
5.1 Computer Programs
5.2 Menu System
6. The Computer Programs NUMINT and LINEAR
6.1 Program NUMINT
6.2 Program LINEAR
7. The Computer Programs SATORB and LEOKIN
7.1 Program SATORB
7.2 Kinematic LEO Orbits: Program LEOKIN
7.3 Dynamic and Reduced Dynamics LEO Orbits
Using Program SATORB
8. The Computer Program ORBDET
8.1 Introduction
8.2 Orbit Determination as a Boundary Value Problem
8.3 Determination of a Circular Orbit
9. The Computer Program ERDROT
9.1 Earth Rotation
9.2 Rotation of the Moon
9.3 The TV Body Problem Earth Moon Sun Planets
9.4 Space Geodetic and Atmospheric Aspects of Earth Rotation
10. The Computer Program PLASYS
11. Elements of Spectral Analysis
and the Computer Program FOURIER
11.1 Statement of the Problem
11.2 Harmonic Analysis Using Least Squares Techniques
11.3 Classical Discrete Fourier Analysis
11.4 Fast Fourier Analysis
11.5 Prograde and Retrograde Motions of Vectors
11.6 The Computer Program FOURIER
References
Abbreviations and Acronyms
Name Index
Subject Index |
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| index_date | 2024-07-02T13:39:48Z |
| indexdate | 2024-07-09T20:33:54Z |
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| spelling | Beutler, Gerhard Verfasser aut Methods of celestial mechanics 1 Physical, mathematical, and numerical principles Gerhard Beutler Berlin [u.a.] Springer 2005 XVI, 464 S. 1 CD-ROM (12 cm) txt rdacontent n rdamedia nc rdacarrier Astronomy and astrophysics library (DE-604)BV021252705 1 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014574066&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Beutler, Gerhard Methods of celestial mechanics |
| title | Methods of celestial mechanics |
| title_auth | Methods of celestial mechanics |
| title_exact_search | Methods of celestial mechanics |
| title_exact_search_txtP | Methods of celestial mechanics |
| title_full | Methods of celestial mechanics 1 Physical, mathematical, and numerical principles Gerhard Beutler |
| title_fullStr | Methods of celestial mechanics 1 Physical, mathematical, and numerical principles Gerhard Beutler |
| title_full_unstemmed | Methods of celestial mechanics 1 Physical, mathematical, and numerical principles Gerhard Beutler |
| title_short | Methods of celestial mechanics |
| title_sort | methods of celestial mechanics physical mathematical and numerical principles |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014574066&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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