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Full Description
This book describes a revolutionary new approach to determining low energy routes for spacecraft and comets by exploiting regions in space where motion is very sensitive (or chaotic). It also represents an ideal introductory text to celestial mechanics, dynamical systems, and dynamical astronomy. Bringing together wide-ranging research by others with his own original work, much of it new or previously unpublished, Edward Belbruno argues that regions supporting chaotic motions, termed weak stability boundaries, can be estimated. Although controversial until quite recently, this method was in fact first applied in 1991, when Belbruno used a new route developed from this theory to get a stray Japanese satellite back on course to the moon. This application provided a major verification of his theory, representing the first application of chaos to space travel. Since that time, the theory has been used in other space missions, and NASA is implementing new applications under Belbruno's direction. The use of invariant manifolds to find low energy orbits is another method here addressed.
Recent work on estimating weak stability boundaries and related regions has also given mathematical insight into chaotic motion in the three-body problem. Belbruno further considers different capture and escape mechanisms, and resonance transitions. Providing a rigorous theoretical framework that incorporates both recent developments such as Aubrey-Mather theory and established fundamentals like Kolmogorov-Arnold-Moser theory, this book represents an indispensable resource for graduate students and researchers in the disciplines concerned as well as practitioners in fields such as aerospace engineering.
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
