Capture Dynamics and Chaotic Motions in Celestial Mechanics
Capture Dynamics and Chaotic Motions in Celestial Mechanics
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DOI：
10.2307/j.ctv301g1f
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发表时间：
2004-01
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影响因子：
--
通讯作者：
E. Belbruno
中科院分区：
文献类型：
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作者：
E. Belbruno
第一章第一章第二章第一章第三章第四章第四章第五章第六章第七章第七章第十一章第十三章介绍N -体问题1 1.1 N -体问题1 1.2平面三体问题9 1.3两体问题11 1.4碰撞的正则化16 1.5限制三体问题：公式24 1.6开普勒问题和等效测地流35第2章.有界运动、康托集和扭曲映射49 2.1拟周期性和KAM定理50 2.2莫泽扭曲定理、康托集59 2.3保面积映射、不动点、双曲性66 2.4周期轨道和椭圆不动点78 2.5奥布里-马瑟集和限制性三体问题91第3章.捕获103 3.1捕获介绍105 3.2弱稳定边界120 3.3主交换捕获的存在性及其应用131 3.4使用弹道捕获的低能月球转移144 3.5抛物线运动，W的双曲扩展156 3.6 W H上双曲网络的存在性165参考文献193索引209
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