Perozzi / Ferraz-Mello Space Manifold Dynamics

Novel Spaceways for Science and Exploration
1. Auflage 2010
ISBN: 978-1-4419-0348-8
Verlag: Springer-Verlag
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 258 Seiten

Autoren/Hrsg.

Perozzi, Ettore

Ferraz-Mello, Sylvio

Inhaltsverzeichnis

1;Preface;5
2;Recommendations;8
3;Contents;10
4;Contributors;12
5;About the Editors;14
6;Invariant Manifolds, Lagrangian Trajectories and Space Mission Design;15
6.1;1 Introduction;15
6.1.1;1.1 The CRTBP and the Libration Points;16
6.1.2;1.2 Properties of the Libration Point Orbits;17
6.2;2 Libration Point Orbits and Their Synthetic Representation;19
6.2.1;2.1 Libration Point Orbits;19
6.2.2;2.2 Synthetic Representations;21
6.2.2.1;2.2.1 Poincaré Map Representation;21
6.2.2.2;2.2.2 Energy vs Rotation Number Representation;22
6.3;3 Computation of LPOs;25
6.3.1;3.1 LindstedtéPoincaré Computation of Tori and Their Stable and Unstable Manifolds;25
6.3.2;3.2 Numerical Computation of Tori and Their Stable and Unstable Manifolds;28
6.4;4 Homoclinic and Heteroclinic Orbits;29
6.5;5 Applications of Invariant Manifolds;31
6.5.1;5.1 Transfers from the Earth;31
6.5.2;5.2 Transfers using invariant manifolds;32
6.5.3;5.3 The TCM Problem;34
6.5.4;5.4 Transfers Between Halo Orbits;39
6.5.5;5.5 Transfers Between Lissajous Orbits;42
6.5.5.1;5.5.1 Effective Phases and Eclipse Avoidance;45
6.5.5.2;5.5.2 Rendez-vous in the Libration Zone;50
6.5.6;5.6 Transfers Between Earth-Moon and Sun-Earth Lissajous Orbits;54
6.6;6 Station Keeping;61
6.6.1;6.1 The Target Mode Approach and the Floquet Mode Approach;61
6.6.2;6.2 Numerical Results;67
6.7;7 Low Energy Transfers and the Weak Stability Boundary;69
6.7.1;7.1 The Weak Stability Boundary;70
6.7.2;7.2 Numerical Determination of WSB and Low Energy Transfers;73
6.7.3;7.3 Solar System Low Energy Transfers and Astronomical Applications;74
6.8;8 Rescue Trajectories from the Moons Surface;76
6.8.1;8.1 Stable Manifolds Associated with Halo Orbits;76
6.8.1.1;8.1.1 Numerical Results;79
6.8.2;8.2 Stable Manifolds Associated with Lissajous Orbits;85
6.8.2.1;8.2.1 Numerical Results;86
6.8.3;8.3 Summary of Results;88
6.9;9 Spacecraft Missions to LPOs;90
6.9.1;9.1 Introduction;90
6.9.2;9.2 Missions to LPO;90
6.9.3;9.3 Mission Design Problems;96
6.9.4;9.4 LPO in Lunar and Exploration Missions;97
6.9.5;9.5 LPO in Mission Recovery;99
6.9.6;9.6 Conclusions;102
6.10;10 Summary and Outlook;102
6.11;References;107
7;Chaos and Diffusion in Dynamical Systems Through Stable-Unstable Manifolds;111
7.1;1 Introduction;111
7.2;2 The Homoclinic Tangle of Hyperbolic Saddle Points;113
7.3;3 From Chaos to Diffusion in two Dimensional Symplectic Maps;116
7.4;4 Higher Dimensional Systems: from Arnolds Model to Four Dimensional Maps;119
7.5;References;125
8;Regular and Chaotic Dynamics of Periodic and Quasi-PeriodicMotions;127
8.1;1 Introduction;127
8.2;2 Around Equilibrium Points;128
8.3;3 From Floquet to Lyapunov;130
8.4;4 Integrable versus NonIntegrable;131
8.5;5 Getting Started with Perturbation Theory;133
8.6;6 Birth and Death of Invariant Tori;135
8.7;7 Diffusion and Exponential Stability;137
8.8;8 Hunting for Periodic Orbits;138
8.9;9 The Lagrangian Solutions;140
8.9.1;9.1 The Restricted, Planar, Circular Lagrangian Solutions;140
8.9.2;9.2 The Restricted, Planar, Elliptic Lagrangian Solutions;143
8.9.3;9.3 The Lagrangian Points in Flight Dynamics;143
8.10;Appendix A. Periodic and QuasiPeriodic Motions;144
8.11;References;145
9;Survey of Recent Results on Weak Stability Boundariesand Applications;147
9.1;1 Introduction;147
9.2;2 Restricted Three-Body Problem Model;149
9.3;3 Determination of the Weak Stability Boundary;151
9.4;4 Chaos Associated with the Weak Stability Boundary and Parabolic Motion;154
9.5;5 Applications to Astronomy;157
9.5.1;5.1 Formation of the Moon;157
9.5.2;5.2 Minimal Energy Transfer of Material Between Planetary Systems;159
9.6;References;160
10;On the Accessibility of the Moon;162
10.1;1 Introduction;162
10.2;2 H-plot;164
10.3;3 SMD Transfers;166
10.4;4 A Lunar Satellite Constellation;167
10.5;5 Mars and Geostationary Missions;169
10.6;6 Concluding Remarks;170
10.7;References;171
11;Optimal Low-Thrust Trajectories to the Interior Earth-Moon Lagrange Point;173
11.1;1 Introduction;173
11.2;2 Governing Equations;175
11.3;3 Numerical Optimization Method;177
11.4;4 Generation of Periodic Orbits;179
11.4.1;4.1 Results;181
11.4.2;4.2 Comparison with Shooting Method;184
11.5;5 Low Thrust Transfer to a Periodic Orbit;187
11.5.1;5.1 Results;192
11.6;6 Conclusions;195
11.7;References;195
12;On the Use of the Earth-Moon Lagrangian Point L1 for Supporting the Manned Lunar Exploration;197
12.1;1 Introduction;197
12.2;2 Transfers Between the Earth and EML1;198
12.2.1;2.1 From the Earth to EML1;198
12.2.2;2.2 From EML1 to the Earth;200
12.3;3 Analysis of Orbital Evolution of Orbits Around EML1;203
12.4;4 Transfers Between EML1 and the Moon;204
12.4.1;4.1 From EML1 to the Lunar Surface;204
12.4.2;4.2 From the Lunar Surface to EML1;207
12.5;5 Summary;210
12.6;References;212
13;Manifolds and Radiation Protection;214
13.1;1 Introduction;214
13.2;2 Classification of Radiation;215
13.2.1;2.1 Ionizing:;215
13.2.2;2.2 Non-Ionizing:;216
13.3;3 Radiation in Space Missions;216
13.4;4 Monitoring Systems on ISS;217
13.5;5 Protecting Space Crews;217
13.6;References;218
14;Three-Body Invariant Manifold Transition with ElectricPropulsion;219
14.1;1 Introduction;219
14.2;2 Mathematical Fundamentals;220
14.2.1;2.1 Circular Restricted Three-Body Model;220
14.2.2;2.2 Reference System Transformation;222
14.2.3;2.3 Thrust Acceleration;223
14.3;3 Interplanetary Phase;223
14.3.1;3.1 Trajectory Optimization;224
14.3.2;3.2 Trajectory Conjunction;224
14.4;4 Uranian Tour;225
14.4.1;4.1 Approach;225
14.4.2;4.2 Tour Optimization;227
14.5;5 Results;228
14.5.1;5.1 Interplanetary Trajectory;228
14.5.2;5.2 Uranian Tour;232
14.6;6 Conclusions;236
14.7;References;237
15;From Sputnik to the Moon: Astrophysics and Cosmologyfrom Space;238
15.1;1 The Birth of Space Astrophysics;238
15.2;2 From Planck to the Moon;240
15.3;3 Why from the Moon;240
15.4;4 CMB Anisotropies;241
15.5;5 CMB Polarization Anisotropy Beyond Planck;242
15.6;6 Small Scale Anisotropy Generated by Sunyaev-Zeldovich Effects;244
15.7;7 A Concept Proposal for a Moon-Based Project Dedicated to CMB Polarization Anisotropy;245
15.8;8 CMB Spectrum;246
15.9;9 CMB Spectrum Beyond COBE/FIRAS;247
15.10;10 A Concept Proposal for a Moon-Based Experiment Dedicated to CMB Spectrum;249
15.11;References;251
16;Space Exploration: How Science and Economy may WorkTogether;253
16.1;1 Why Space Exploration?;253
16.2;2 Space Exploration as a Challenge and an Opportunity for Europe;254
16.3;3 The Importance of Public Awareness;254
16.4;4 The Impact of Science;256
16.5;5 Manned Space Exploration Constraints;257
16.6;6 Economy and Science;257
16.7;7 Conclusions;260
16.8;References;261
17;Index;262