Modern Astrodynamics (eBook)

Front Cover 1
Title Page 4
Copyright Page 5
Table of Contents 6
Foreword 10
Introduction 12
Chapter 1 Perturbed Motion 16
1.1 Basic definitions 16
1.2 Forces 18
1.3 Gravity 19
1.4 Drag 22
1.5 3-Body 27
1.6 Solar radiation pressure 27
1.7 Tides 28
1.8 Albedo 29
1.9 Other 29
1.10 Propagating the orbit 30
1.11 Analytical 30
1.12 Numerical 30
1.13 Semianalytical 31
1.14 Variation of parameters 31
1.15 Lagrangian VOP—conservative forces 32
1.16 Gaussian VOP—nonconservative forces 33
1.17 Effect on orbits 34
1.18 J2 Only 34
1.19 Comparative force model effects 35
1.20 Conclusions 36
References 36
Chapter 2 Gauge Freedom in Astrodynamics 38
2.1 Introduction 38
2.2 Gauge freedom in the theory of orbits 49
2.3 A practical example on gauges: a satellite orbiting a precessing oblate planet 54
2.4 Conclusions: how we benefit from the gauge freedom 63
Appendix 1. Mathematical formalities: Orbital dynamics inthe normal form of Cauchy 64
Appendix 2. Precession of the equator of date relative tothe equator of epoch 65
References 66
Chapter 3 Solving Two-Point Boundary Value ProblemsUsing Generating Functions: Theory and Applicationsto Astrodynamics 68
3.1 Introduction 68
3.2 Solving two-point boundary value problems 71
3.3 Hamilton’s principal function 89
3.4 Local solutions of the Hamilton–Jacobi equation 92
3.5 Applications 105
3.6 Conclusions 113
Appendix A. The Hamilton–Jacobi equation at higher orders 114
Appendix B. The Hill three-body problem 117
References 119
Chapter 4 Low-Energy Transfers and Applications 122
4.1 Introduction 122
4.2 Capture problem, models, and transfer types 123
4.3 Ballistic capture regions and transfers 127
4.4 Chaos and weak capture 135
4.5 Origin of the Moon 138
References 140
Chapter 5 Set Oriented Numerical Methods in Space Mission Design 142
5.1 Introduction 142
5.2 Dynamical systems and mission design 142
5.3 Set oriented numerics 145
5.4 Computing invariant manifolds 150
5.5 Detecting connecting orbits 154
5.6 Extension to controlled systems 160
5.7 Conclusion 166
References 166
Chapter 6 Space Trajectory Optimization and L1-OptimalControl Problems 170
6.1 Introduction 170
6.2 Geometry and the mass flow equations 173
6.3 Cost functions and Lebesgue norms 175
6.4 Double integrator example 179
6.5 Issues in solving nonlinear L1-optimal control problems 185
6.6 Solving nonlinear L1-optimal control problems 190
6.7 L1-Formulation of the minimum-fuel orbit transfer problem 194
6.8 A simple extension to distributed space systems 196
6.9 Conclusions 200
References 201
Chapter 7 Orbital Mechanics of Propellantless Propulsion Systems 204
7.1 Introduction 204
7.2 Solar sailing 205
7.3 Solar sail orbital mechanics 210
7.4 Artificial three-body equilibria for solar sails 213
7.5 Mission applications 218
7.6 Tethers in space 223
7.7 Tethers in orbit 232
7.8 Conclusions 247
References 248
Chapter 8 Cooperative Spacecraft Formation Flying: Model PredictiveControl with Open- and Closed-Loop Robustness 252
8.1 Introduction 252
8.2 Dynamics of formation flight 254
8.3 Formation flight control and the model predictive control formulation 258
8.4 Distributed coordination through virtual center 264
8.5 Open loop robust control and replan frequency 275
8.6 Using closed-loop robust MPC 280
8.7 Conclusions 288
8.8 Nomenclature 289
References 289
Index 294
Color Plate 300