Author(s): Wang Sang Koon, Martin W. Lo, Jerrold E. Marsden
Year: 2009
Language: English
Pages: 336
Preface......Page 11
Astrodynamics and Dynamical Astronomy......Page 15
The Patched Three-Body Approximation......Page 18
Organization of the Book......Page 32
Introduction......Page 37
Planar Circular Restricted Three-Body Problem......Page 38
Equations of Motion......Page 40
Energy Surface and Realms of Possible Motion......Page 48
Location of the Equilibrium Points......Page 52
Linearization near the Collinear Equilibria......Page 56
Geometry of Solutions near the Equilibria......Page 60
Flow Mappings in the Equilibrium Region......Page 66
Trajectories in the Neck Region......Page 68
Introduction.......Page 71
Existence of Orbits Homoclinic to the Lyapunov Orbit......Page 74
Existence of Transversal Homoclinic Orbits in the Interior Realm......Page 80
Existence of Transversal Homoclinic Orbits in the Exterior Realm......Page 84
Existence of Heteroclinic Connections between Lyapunov Orbits......Page 86
Construction of a Suitable Poincaré Map......Page 90
Horseshoe-like Dynamics......Page 95
Symbolic Dynamics......Page 102
Global Orbit Structure......Page 105
Introduction......Page 109
Differential Correction......Page 111
Basic Theory on Invariant Manifolds of a Periodic Orbit......Page 114
Trajectories with Prescribed Itineraries......Page 121
Example Itinerary: (X,J,S,J,X)......Page 133
Introduction......Page 137
Modeling the Four-Body Problem......Page 139
Bicircular Model......Page 140
Example 1: Low-Energy Transfer to the Moon......Page 145
Example 2: The Lunar L1 Gateway Station......Page 151
Introduction......Page 157
Some History of Halo Orbits for Space Missions......Page 158
A Few Basic Facts About the CR3BP......Page 160
Overview of Halo Orbit Computations......Page 163
Periodic Orbits and the Lindstedt-Poincaré Method......Page 166
Third-Order Richardson Expansion......Page 170
Numerical Computation of Halo Orbits......Page 174
Libration Orbits near Collinear Points......Page 177
Computation of Libration Orbits in the Center Manifold......Page 181
Introduction......Page 187
Computation of Invariant Manifolds Associated to a Halo Orbit......Page 190
Earth-to-Halo Differential Corrector......Page 192
Numerical Results......Page 198
Return Trajectory Differential Correction......Page 202
Introduction......Page 211
Halo Orbit Mission Correction Maneuvers......Page 213
Optimal Control for Transfer Correction Maneuvers......Page 215
Numerical Results for the Halo Orbit Insertion Problem......Page 221
Numerical Results for the Stable Manifold Orbit Insertion Problem......Page 230
Station-Keeping with the Target Point Approach......Page 234
Station-Keeping with Floquet Mode Approach......Page 237
Introduction......Page 241
The Linearized Hamiltonian System......Page 243
Invariant Manifold as Separatrix......Page 249
Construction of Orbits with Prescribed Itineraries in the Spatial Case......Page 254
From Ganymede to High Inclination Europa Orbit......Page 262
Normal Form Computations......Page 265
Reduction to the Center Manifold......Page 269
NHIM and its Stable and Unstable Manifolds......Page 272
Multi-Moon Orbiters and Low Thrust Trajectories......Page 275
Introduction to Multi-Moon Orbiter Design......Page 276
Inter-Moon Transfer Via the Resonant Structure of Phase Space......Page 280
Lobe Dynamics and Resonant Gravity Assists......Page 285
Trade-Off: V vs. Time of Flight......Page 292
Some Open Problems for Multi-Moon Orbiters......Page 298
Low Thrust Trajectories......Page 300
How This Book Fits into the Larger Body of Literature......Page 307
Index......Page 313
