航天器姿态动力学中的混沌

Chapter 1 Primer on Spacecraft Dynamics

1.1 Orbital Motionof Spacecraft

1.1.1 Gravitational Field of a Particle,

1.1.2 Gravitational Field of a Rigid Body

1.1.3 Dynamical Equations of Two-body System

1.1.4 Firstlntegrals

1.1.5 Characteristics ofKeplerian Orbit

1.1.6 Elliptic Orbit

1.2 Environmental Torques Acting on Spacecraft

1.2.1 Gravitational Torque

1.2.2 Magnetic Torque

1.3 Attitude Motion of Spacecraft in the Gravitational Field

1.3.1 Euler's Equations and Poisson's Equations

1.3.2 Planar Libration

1.3.3 Stability of Relative Equilibrium

1.3.4 Attitude Motion of a Gyrostat

1.4 Attitude Motion of Torque-free Spacecraft

1.4.1 Torque-free Rigid Body,

1.4.2 Torque free Gyrostat

1.4.3 Influence of Energy Dissipation on Spinning Spacecraft

References

Chapter 2 A Survey of Chaos Theory

2.1 The Overview of Chaos

2.1.1 DescriptionsofChaos

2.1.2 Geometrical Structures of Chaos

2.1.3 Routes to Chaos

2.2 Numeri calIdentification of Chaos

2.2.1 Introduction

2.2.2 Lyapunov Exponents

2.2.3 Power Spectra

2.3 Melnikov Theory

2.3.1 Introduction

2.3.2 Transversal Homoclinic/Heteroclinic Point

2.3.3 Analytical Prediction

2.3.4 Interruptions

2.4 Chaos in Hamiltonian Systems

2.4.1 Hamiltonian Systems,lntegrability and KAM Theorem

2.4.2 Stochastic Layers and Global Chaos

2.4.3 Arnol'dDiffusion

2.4.4 Higher-Dimensional Version ofMelnikov Theory

References

Chapter 3 Chaos in Planar Attitude Motion of Spacecraft

3.1 Rigid Spacecraft in an Elliptic Orbit

3.1.1 Introduction

3.1.2 Dynamical Model

3.1.3 MelnikovAnalysis

3.1.4 Numerical Simulations

3.2 Tethered Satellite Systems

3.2.1 Introductio

3.2.2 DynamicaI Models

3.2.3 MelnikovAnalysis of the Uncoupled Case

3.2.4 Numerical Simulations

3.3 Magnetic Rigid Spacecraft in a Circular Orbit

3.3.1 Introductio

3.3.2 Dynamical Model

3.3.3 MelnikovAnalysis

3.3.4 Numericallnvestigations: Undamped Case

3.3.5 Numericallnvestigations: Damped Case

3.4 Magnetic Rigid Spacecraft in an Elliptic Orbit

3.4.1 Introductio

3.4.2 Dynamical Model

3.4.3 Melnikov Analysis

3.4.4 Numerical Simulations

References

Chapter 4 Chaos in SpatiaIAffitude Motion of Spacecraft

4.1 Attitude Motion Describedby Serret-AndoyerVariables

4.1.1 Serret-AndoyerVariables

4.1.2 Torque-free Rigid Body

4.1.3 Torque-freeGyrostat

4.1.4 Gyrostat in the Gravitational Field

4.1.5 Influence ofthe Geomagnetic Field

4.2 Rigid-body Spacecraftin an Elliptic Orbit

4.2.1 Introduction

……

Chapter 5 Control of Chaotic Attitude Motion

航天器混沌姿态运动的识别和控制问题在航天科学中具有重要实际意义。《航天器姿态动力学中的混沌》致力于总结该领域的近期发展，提供研究航天器姿态运动的新方法和观点，也为该领域进一步的深入分析研究提供有明确工程背景的新的数学模型。读者可从《航天器姿态动力学中的混沌》获得混沌和混沌控制理论及其在航天器姿态运动中应用的知识，包括基本概念，主要方法以及最新进展。

Attitude dynamics is the theoretica·basis of attitude contro·of spacecrafts in aerospace engineering. With the development of nonlinear dynamics, chaos in spacecraft attitude dynamics has drawn great attention since the iggo's. The problem of the predictability and controllability of the chaotic attitude motion of a spacecraft has a practica·significance in astronautic science. Ihis book aims to summarize basic concepts, main approaches,and recent progress in this area. It focuses on the research work of the author and other Chinese scientists in this field, providing new methods and viewpoints in the investigation of spacecraft attitude motion, as wel·as new mathematica·models, with definite engineering backgrounds, for further analysis.
　Professor Yanzhu Liu was the Director of the Institute of Engineering Mechanics, Shanghai Jiao Tong University, China. Dr. Liqun Chen is a Professor at the Department of Mechanics, Shanghai University, China.