Spacecraft Formation Flying: Dynamics, Control and Navigation Book

1 Introduction 1

2 Fundamental Astrodynamics 13

3 The Basics of Analytical Mechanics, Optimization, Control and Estimation 39

4 Nonlinear Models of Relative Dynamics 59

5 Linear Equations of Relative Motion 83

6 Modeling Relative Motion Using Orbital Elements 123

7 Modeling Perturbed Relative Motion Using Orbital Elements 143

8 Perturbation Mitigation 185

9 Rotation-Translation Coupling 227

10 Formation Control 241

11 Implementation of [Delta][actual symbol not reproducible] Commands 271

12 Relative Measurements and Navigation 287

13 High-Fidelity Formation Flying Simulation 305

14 Summary and Future Prospects 329

Appendix A The Transformation Matrix [Sigma](t) 331

Appendix B The Transformation Matrix [Sigma](t)[superscript -1] 332

Appendix C The Matrix [actual symbol not reproducible](t) 334

Appendix D The State Transition Matrix for Relative Mean Elements 335

Appendix E Transformation from Mean to Osculating Elements 338

Appendix F Jacobian for Mean to Osculating Elements 341

Appendix G Small Eccentricity Theory 351

Appendix H Yan-Alfriend Nonlinear Theory Coefficients 357

References 363

Index 379