Capture Dynamics and Chaotic Motions in Celestial Mechanics

By E. Belbruno. 2004

181 citations recorded by the source corpus.

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

Subfields: Astronomy and Astrophysics

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In Astronomy and Astrophysics

Citations in the corpus

Cooperative Filters and Control for Cooperative Exploration (2010, unknown): “[37], [38], [50]–[52] and the references therein.”
On optimal two-impulse Earth–Moon transfers in a four-body model (2013, methodology): “They exploit the concept of temporary ballistic capture, or weak capture, which is defined in the framework of n-body problems (Belbruno 2004).”
The Restricted Three-Body Problem and Holomorphic Curves (2018, background): “It was Belbruno who found the ﬁrst realistic low energy transit orbit from an orbit around the earth to an orbit around the moon [31, 32].”