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Preface
The development of spacecraft has drawn considerable attentions in the field of dynamics since the 1950s. The spacecraft can be regarded as a particle or as a body, depending on whether one focuses on the spacecraft’s orbital motion or on its rotational motion about the center of mass. Spacecraft attitude dynamics deals with the rotational motion of spacecraft. In the discussion of attitude dynamics, the rotation of spacecraft is usually assumed not to alter the orbit, while the orbit sometimes influences the rotational motion. Almost all spacecraft have some attitude requirements, either explicit pointing requirements for antennas or cameras, requirements for solar panel orientation, or simply a requirement for a given spin-axis direction. All the requirements are implemented by the design of attitude controls. The strategies chosen in the control process may limit the useful lifetime of the spacecraft, since an all-thruster control system depletes its propellant supply. Attitude dynamics forms a theoretical basis of the design and control of spacecraft. The present monograph is concerned with spacecraft attitude motion, although essential elements of orbital dynamics will be introduced and the effects of orbital motion will be included in a few cases.
With the development of nonlinear dynamics, chaos in spacecraft attitude dynamics has stirred renewed interests since the 1990s. In fact, for astronautical investigations, the predictability of spacecraft rotations is critical, and thus chaotic motions must be avoided. On the other hand, there are scientific experiments that require the whole celestial sphere to be scanned, and in those cases the chaotic rotation may be desirable. Therefore chaos theory offers a new method and viewpoint for designing spacecraft. In addition, spacecraft attitude dynamics also provides new mathematical models for engineering application of chaos analysis. Although there are some excellent monographs and textbooks on spacecraft attitude dynamics, there are few treatises on chaotic attitude motion. The present monograph focuses on chaos in spacecraft attitude dynamics.
The monograph begins with the necessary fundamentals. Chapter 1 provides a
Chaos in Attitude Dynamics of Spacecraft
primer on spacecraft dynamics, and Chapter 2 presents a survey of chaos theory. Different chaotic attitude motions are treated in Chapters 3 and 4. Chapter 3 considers only the planar motion of spacecraft, while Chapter 4 covers the spatial motion. The monograph ends with Chapter 5, dealing with controlling chaotic attitude motion.
The main goal of the monograph is to provide readers with the knowledge of theory and application of chaos and its control in spacecraft attitude dynamics, including the basic concepts, main approaches and the latest research progress. The material is appropriate for university teachers, scientists, engineers, and graduate students in the fields of mechanics, applied mathematics, and aerospace science.
Except for some background presented in Chapters 1 and 2, as well as Sections
4.1 and 5.1, all other materials contained in the monograph are adopted from research papers of the authors and their co-workers. The research work was financially supported by the National Natural Science Foundation of China (Project Nos. 19782003 and 10082003), the National Outstanding Young Scientists Foundation of China (Project No. 10725209), Shanghai Municipal Development Foundation of Science and Technology (Project Nos. 98JC14032 and 98SHB1417), Shanghai Municipal Education Commission Scientific Research Project (No. 2000A12), and Shanghai Leading Academic Discipline Project (No. Y0103).
 

Chapter 1 Primer on Spacecraft Dynamics 
1.1 Orbital Motion of 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 First Integrals 
1.1.5 Characteristics of Keplerian 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 Descriptions of Chaos 
2.1.2 Geometrical Structures of Chaos 
2.1.3 Routes to Chaos 
2.2 Numerical Identification 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, Integrability and KAM Theorem 
2.4.2 Stochastic Layers and Global Chaos 
2.4.3 Arnol'd Diffusion 
2.4.4 Higher-Dimensional Version of Melnikov 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 Melnikov Analysis 
3.1.4 Numerical Simulations 
3.2 Tethered Satellite Systems 
3.2.1 Introduction 
3.2.2 Dynamical Models 
3.2.3 Melnikov Analysis of the Uncoupled Case 
3.2.4 Numerical Simulations 
3.3 Magnetic Rigid Spacecraft in a Circular Orbit 
3.3.1 Introduction 
3.3.2 Dynamical Model 
3.3.3 Melnikov Analysis 
3.3.4 Numerical Investigations: Undamped Case 
3.3.5 Numerical Investigations: Damped Case 
3.4 Magnetic Rigid Spacecraft in an Elliptic Orbit 
3.4.1 Introduction 
3.4.2 Dynamical Model 
3.4.3 Melnikov Analysis 
3.4.4 Numerical Simulations 
References 
Chapter 4 Chaos in Spatial Attitude Motion of Spacecraft 
4.1 Attitude Motion Described by Serret-Andoyer Variables 
4.1.1 Serret-Andoyer Variables 
4.1.2 Torque-free Rigid Body 
4.1.3 Torque-free Gyrostat 
4.1.4 Gyrostat in the Gravitational Field 
4.1.5 Influence of the Geomagnetic Field 
4.2 Rigid-body Spacecraft in an Elliptic Orbit 
4.2.1 Introduction 
4.2.2 Dynamical Model 
4.2.3 Melnikov Analysis 
4.2.4 Numerical Simulations 
4.3 Rigid-body Spacecraft with an Eccentrically Rotating Mass 
4.3.1 Introduction 
4.3.2 Dynamical Model 
4.3.3 Melnikov Analysis 
4.3.4 Numerical Simulations 
4.4 Magnetic Gyrostat Spacecraft in a Circular Orbit 
4.4.1 Introduction 
4.4.2 Unperturbed Motion of a Gyrostat 
4.4.3 Melnikov Analysis 
4.4.4 Numerical Simulations 
References 
Chapter 5 Control of Chaotic Attitude Motion 
5.1 Control of Chaos:An Overview 
5.1. 1 Introduction 
5.1.2 Problem Formulations 
5.1.3 OGY Method and Its Generalization 
5.1.4 Synchronization: Chaos Control in a Broader Sense 
5.2 The Parametric Open-plus-closed-loop Method 
5.2.1 Introduction 
5.2.2 The Control Law 
5.2.3 Numerical Examples 
5.2.4 Discussions 
5.3 The Stability Criterion Method 
5.3.1 Introduction 
5.3.2 The Control Law 
5.3.3 Numerical Examples 
5.4 Controlling Chaotic Attitude Motions 
5.4.1 Introduction 
5.4.2 Dynamical Model of Controlled Spacecraft 
5.4.3 Applications of the Parametric Open-plus-closed-loop Method 
5.4.4 Applications of the Stability Criterion Method 
References

Publisher:  Tsinghua University Press 
Edition   1st edition

The first author thanks his former PhD students Professor Peng Jianhua, Professor Chen Liqun, Dr. Cheng Gong, and his postdoctoral fellow Professor Yu Hongjie for their collaborations on related research. The second author thanks Professor Liu Yanzhu, who, serving as his PhD supervisor, introduced him to this field. He also thanks his hosts, Professor Jean W. Zu (University of Toronto) and Professor C. W. Lim (City University of Hong Kong) for their assistance during his visit to their institutes so that he could complete his portions of the book.

The authors thank Tsinghua University Press and Springer for the publication of this book. They also thank Shanghai Jiao Tong University for partial financial support of the publication. Yanzhu Liu (Shanghai Jiao Tong University) Liqun Chen (Shanghai University)