| | TABLE OF CONTENTS: List of Figures vii
Foreword xi
Preface xiii
Chapter 1. Introduction to the N -Body Problem 1
1.1 The N -Body Problem 1
1.2 Planar Three-Body Problem 9
1.3 Two-Body Problem 11
1.4 Regularization of Collision 16
1.5 The Restricted Three-Body Problem: Formulations 24
1.6 The Kepler Problem and Equivalent Geodesic Flows 35
Chapter 2. Bounded Motion, Cantor Sets, and Twist Maps 49
2.1 Quasi-Periodicity and the KAM Theorem 50
2.2 The Moser Twist Theorem, Cantor Sets 59
2.3 Area-Preserving Maps, Fixed Points, Hyperbolicity 66
2.4 Periodic Orbits and Elliptic Fixed Points 78
2.5 Aubrey-Mather Sets and the Restricted Three-Body Problem 91
Chapter 3. Capture 103
3.1 Introduction to Capture 105
3.2 The Weak Stability Boundary 120
3.3 Existence of Primary Interchange Capture and an Application 131
3.4 A Low Energy Lunar Transfer Using Ballistic Capture 144
3.5 Parabolic Motion, Hyperbolic Extension of W 156
3.6 Existence of a Hyperbolic Network on W H 165
Bibliography 193
Index 209
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