What is included with this book?
Foreword | p. xiii |
Preface | p. xv |
Introduction | p. 1 |
What is Spacecraft Formation Flying? | p. 1 |
Coordination Approaches | p. 2 |
Fuel-use Drivers | p. 3 |
Control of Spacecraft Formations | p. 4 |
Control Approaches | p. 5 |
Space Navigation and the Global Positioning System | p. 7 |
Formation Flying Missions | p. 8 |
Fundamental Astrodynamics | p. 13 |
Coordinate Systems | p. 14 |
The Keplerian Two-body Problem | p. 16 |
Solution of the Inertial Equations of Motion | p. 22 |
Nonsingular Orbital Elements | p. 25 |
Non-Keplerian Motion and Orbital Perturbations | p. 28 |
Averaging Theory | p. 36 |
The Basics of Analytical Mechanics, Optimization, Control and Estimation | p. 39 |
Lagrangian and Hamiltonian Mechanics | p. 39 |
The Delaunay Elements | p. 41 |
Canonical Transformations | p. 42 |
Brouwer Theory | p. 43 |
Constrained Static Optimization | p. 46 |
Control Lyapunov Functions | p. 47 |
Linear Quadratic Regulation | p. 48 |
Kalman Filtering | p. 49 |
The Unscented Kalman Filter | p. 52 |
Nonlinear Models of Relative Dynamics | p. 59 |
Equations of Relative Motion in the Unperturbed Case | p. 60 |
The Energy Matching Condition | p. 64 |
Impulsive Formation-keeping | p. 66 |
Another Outlook on Optimal Formation-keeping | p. 72 |
Circular Chief Orbit | p. 74 |
Lagrangian and Hamiltonian Derivations | p. 76 |
Equations of Relative Motion under the Influence of J_{2} | p. 78 |
Linear Equations of Relative Motion | p. 83 |
The Clohessy-Wiltshire Equations | p. 84 |
Two-impulse Linear Rendezvous | p. 90 |
Lagrangian and Hamiltonian Derivations of the CW Equations | p. 94 |
Accommodating second-order nonlinearities | p. 97 |
Curvilinear vs. Cartesian Relative Coordinates | p. 99 |
Elliptic Reference Orbits | p. 103 |
Periodic Solutions to the TH Equations | p. 117 |
Modeling Relative Motion Using Orbital Elements | p. 123 |
General Solution to the Nonlinear Relative Motion Equations | p. 124 |
Bounds on Maximal and Minimal Distances | p. 128 |
Relative Motion Approximations with a Circular-Equatorial Reference Orbit | p. 129 |
Establishing the PCO Initial Conditions | p. 136 |
Hybrid Differential Equations with Non-linearity Compensation for Unperturbed Circular Orbits | p. 138 |
Modeling Perturbed Relative Motion Using Orbital Elements | p. 143 |
The Unit-Sphere Approach | p. 143 |
Relative Motion Description using Quaternions | p. 147 |
The Gim-Alfriend Geometric Method | p. 150 |
Averaged Relative Motion | p. 165 |
Linearized J2-Dirferential Equations for Circular Orbits | p. 169 |
Differential Equations from the Gim-Alfriend STM | p. 176 |
A Second-Order State Propagation Model | p. 180 |
Perturbation Mitigation | p. 185 |
Dynamic Constraints for J_{2} Mitigation | p. 185 |
A Nonlinear Theory based on Orbital Elements | p. 199 |
Dynamic Model Error Effect Comparison | p. 206 |
Perturbed Fundamental Frequencies for Formations in Near-circular Orbits | p. 212 |
Selection of the PCO Initial Conditions for Near-Circular Orbits | p. 214 |
Matching the In-plane and Cross-track Fundamental Frequencies | p. 216 |
PCO Formation Maintenance based on the Modified CW Equations | p. 219 |
Fuel Minimization and Balancing | p. 222 |
Rotation-Translation Coupling | p. 227 |
Relative Dynamics | p. 228 |
Kinematically-Coupled Relative Spacecraft Motion Model | p. 232 |
Formation Control | p. 241 |
Continuous Control | p. 241 |
Discrete-time LQR Control | p. 249 |
Impulsive Control based on Gauss' Variational Equations | p. 252 |
Two-impulse Formation Reconfiguration for Circular Orbits | p. 256 |
Two-impulse-per-orbit Formation Maintenance | p. 257 |
Implementation of żż Commands | p. 271 |
Plan Implementation | p. 272 |
Impact on Autonomous Rendezvous and Docking | p. 279 |
Relative Measurements and Navigation | p. 287 |
Dynamical Modeling | p. 288 |
Measurement Update: Carrier-Phase Differential GPS | p. 290 |
Comparison of EKF and UKF for Relative Navigation | p. 293 |
High-Fidelity Formation Flying Simulation | p. 305 |
Simulation Controller Configuration | p. 306 |
Simulation Results | p. 308 |
Summary and Future Prospects | p. 329 |
Risk Reduction | p. 329 |
Fuel Requirements | p. 330 |
Mission Operations | p. 330 |
Appendices | p. 331 |
The Transformation Matrix &SIGMA;(t) | p. 331 |
The Transformation Matrix &SIGMA;(t) -1 | p. 332 |
The Matrix B(t) | p. 334 |
The State Transition Matrix for Relative Mean Elements | p. 335 |
Transformation from Mean to Osculating Elements | p. 338 |
Jacobian for Mean to Osculating Elements | p. 341 |
Small Eccentricity Theory | p. 351 |
Yan-Alfriend Nonlinear Theory Coefficients | p. 357 |
References | p. 363 |
Index | p. 379 |
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