| Physical, Mathematical, and Numerical Principles | |
| Overview of the Work | p. 3 |
| Part I: Theory | p. 3 |
| Part II: Applications | p. 9 |
| Part III: Program System | p. 14 |
| Historical Background | p. 19 |
| Milestones in the History of Celestial Mechanics of the Planetary System | p. 19 |
| The Advent of Space Geodesy | p. 31 |
| The Equations of Motion | p. 45 |
| Basic Concepts | p. 46 |
| The Planetary System | p. 50 |
| Equations of Motion of the Planetary System | p. 51 |
| First Integrals | p. 55 |
| The Earth-Moon-Sun-System | p. 61 |
| Introduction | p. 61 |
| Kinematics of Rigid Bodies | p. 63 |
| The Equations of Motion in the Inertial System | p. 71 |
| The Equations of Motion in the Body-Fixed Systems | p. 78 |
| Development of the Equations of Motion | p. 80 |
| Second Order Differential Equations for the Euler Angles ¿, ¿ and ¿ | p. 90 |
| Kinematics of the Non-Rigid Earth | p. 91 |
| Liouville-Euler Equations of Earth Rotation | p. 94 |
| Equations of Motion for an Artificial Earth Satellite | p. 96 |
| Introduction | p. 96 |
| Equations for the Center of Mass of a Satellite | p. 97 |
| Attitude of a Satellite | p. 110 |
| Relativistic Versions of the Equations of Motion | p. 116 |
| The Equations of Motion in Overview | p. 120 |
| The Two- and the Three-Body Problems | p. 123 |
| The Two-Body Problem | p. 123 |
| Orbital Plane and Law of Areas | p. 123 |
| Shape and Size of the Orbit | p. 125 |
| The Laplace Integral and the Laplace Vector q | p. 130 |
| True Anomaly v as a Function of Time: Conventional Approaches | p. 132 |
| True Anomaly v as a Function of Time: Alternative Approaches | p. 137 |
| State Vector and Orbital Elements | p. 140 |
| State Vector → Orbital Elements | p. 142 |
| Orbital elements → State Vector | p. 143 |
| Osculating and Mean Elements | p. 144 |
| The Relativistic Two-Body Problem | p. 147 |
| The Three-Body Problem | p. 150 |
| The General Problem | p. 152 |
| The Problème Restreint | p. 155 |
| Variational Equations | p. 175 |
| Motivation and Overview | p. 175 |
| Primary and Variational Equations | p. 176 |
| Variational Equations of the Two-Body Problem | p. 183 |
| Elliptic Orbits | p. 186 |
| Parabolic Orbits | p. 190 |
| Hyperbolic Orbits | p. 192 |
| Summary and Examples | p. 193 |
| Variational Equations Associated with One Trajectory | p. 195 |
| Variational Equations Associated with the N-Body Problem | p. 198 |
| Efficient Solution of the Variational Equations | p. 202 |
| Trajectories of Individual Bodies | p. 203 |
| The N-Body Problem | p. 205 |
| Variational Equations and Error Propagation | p. 206 |
| Theory of Perturbations | p. 209 |
| Motivation and Classification | p. 209 |
| Encke-Type Equations of Motion | p. 211 |
| Gaussian Perturbation Equations | p. 215 |
| General Form of the Equations | p. 215 |
| The Equation for the Semi-major Axis a | p. 217 |
| The Gaussian Equations in Terms of Vectors h, q | p. 218 |
| Gaussian Perturbation Equations in Standard Form | p. 223 |
| Decompositions of the Perturbation Term | p. 228 |
| Lagrange's Planetary Equations | p. 232 |
| General Form of the Equations | p. 232 |
| Lagrange's Equation for the Semi-major Axis a | p. 234 |
| Lagrange's Planetary Equations | p. 234 |
| First- and Higher-Order Perturbations | p. 240 |
| Development of the Perturbation Function | p. 242 |
| General Perturbation Theory Applied to Planetary Motion | p. 243 |
| Perturbation Equation for the Mean Anomaly ¿(t) | p. 247 |
| Numerical Solution of Ordinary Differential Equations: Principles and Concepts | p. 253 |
| Introduction | p. 253 |
| Mathematical Structure | p. 255 |
| Euler's Algorithm | p. 259 |
| Solution Methods in Overview | p. 264 |
| Collocation Methods | p. 264 |
| Multistep Methods | p. 266 |
| Taylor Series Methods | p. 269 |
| Runge-Kutta Methods | p. 271 |
| Extrapolation Methods | p. 275 |
| Comparison of Different Methods | p. 277 |
| Collocation | p. 279 |
| Solution of the Initial Value Problem | p. 280 |
| The Local Boundary Value Problem | p. 283 |
| Efficient Solution of the Initial Value Problem | p. 285 |
| Integrating a Two-Body Orbit with a High-Order Collocation Method: An Example | p. 291 |
| Local Error Control with Collocation Algorithms | p. 295 |
| Multistep Methods as Special Collocation Methods | p. 304 |
| Linear Differential Equation Systems and Numerical Quadrature | p. 312 |
| Introductory Remarks | p. 312 |
| Taylor Series Solution | p. 313 |
| Collocation for Linear Systems: Basics | p. 315 |
| Collocation: Structure of the Local Error Function | p. 317 |
| Collocation Applied to Numerical Quadrature | p. 320 |
| Collocation: Examples | p. 324 |
| Error Propagation | p. 330 |
| Rounding Errors in Digital Computers | p. 332 |
| Propagation of Rounding Errors | p. 334 |
| Propagation of Approximation Errors | p. 341 |
| A Rule of Thumb for Integrating Orbits of Small Eccentricities with Constant Stepsize Methods | p. 348 |
| The General Law of Error Propagation | p. 350 |
| Orbit Determination and Parameter Estimation | p. 355 |
| Orbit Determination as a Parameter Estimation Problem | p. 355 |
| The Classical Pure Orbit Determination Problem | p. 356 |
| Solution of the Classical Orbit Improvement Problem | p. 357 |
| Astrometric Positions | p. 363 |
| First Orbit Determination | p. 366 |
| Determination of a Circular Orbit | p. 369 |
| The Two-Body Problem as a Boundary Value Problem | p. 373 |
| Orbit Determination as a Boundary Value Problem | p. 378 |
| Examples | p. 381 |
| Determination of a Parabolic Orbit | p. 384 |
| Gaussian- vs. Laplacian-Type Orbit Determination | p. 388 |
| Orbit Improvement: Examples | p. 396 |
| Parameter Estimation in Satellite Geodesy | p. 404 |
| The General Task | p. 405 |
| Satellite Laser Ranging | p. 406 |
| Scientific Use of the GPS | p. 413 |
| Orbit Determination for Low Earth Orbiters | p. 423 |
| References | p. 441 |
| Abbreviations and Acronyms | p. 449 |
| Name Index | p. 453 |
| Subject Index | p. 455 |
| Table of Contents provided by Ingram. All Rights Reserved. |
