Chaos in Attitude Dynamics of Spacecraft

174 Pages·2013·2.572 MB·English

by  Yanzhu Liu, Liqun Chen (auth.)

Yanzhu Liu
Liqun Chen
ChaosW OiRnLDS Attitude
Dynamics of
Spacecraft
123
Yanzhu Liu
Liqun Chen

Chaos in Attitude Dynamics of Spacecraft
Yanzhu Liu
Liqun Chen

Chaos in Attitude
Dynamics of Spacecraft

With 86 figures

DIGITALWORLDS
Authors:

Yanzhu Liu Liqun Chen
Department of Engineering Mechanics Department of Mechanics
Shanghai Jiao Tong University Shanghai University
Shanghai, China Shanghai, China
E-mail: [email protected] E-mail: [email protected]

ISBN 978-7-302-28298-3
Tsinghua University Press, Beijing

ISBN 978-3-642-30079-0 ISBN 978-3-642-30080-6 (eBook)
Springer Heidelberg New York Dordrecht London

Library of Congress Control Number: 2012937465

(cid:2) Tsinghua University Press, Beijing and Springer-Verlag Berlin Heidelberg 2013
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Yanzhu Liu
Liqun Chen

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Chaos in Attitude Dynamics of
Spacecraft
Yanzhu Liu
Liqun Chen

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Chaos in Attitude Dynamics of
Spacecraft

With 86 figures

DIGITALWORLDS
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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). 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)(cid:3)

ii
Contents

Chapter 1(cid:3) Primer on Spacecraft Dynamics....................................................1
1.1(cid:3) Orbital Motion of Spacecraft..................................................................2
1.1.1(cid:3) Gravitational Field of a Particle..................................................2
1.1.2(cid:3) Gravitational Field of a Rigid Body............................................2
1.1.3(cid:3) Dynamical Equations of Two-body System................................4
1.1.4(cid:3) First Integrals..............................................................................5
1.1.5(cid:3) Characteristics of Keplerian Orbit..............................................8
1.1.6(cid:3) Elliptic Orbit.............................................................................10
1.2(cid:3) Environmental Torques Acting on Spacecraft......................................12
1.2.1(cid:3) Gravitational Torque.................................................................12
1.2.2(cid:3) Magnetic Torque.......................................................................15
1.3(cid:3) Attitude Motion of Spacecraft in the Gravitational Field.....................17
1.3.1(cid:3) Euler’s Equations and Poisson’s Equations..............................17
1.3.2(cid:3) Planar Libration........................................................................19
1.3.3(cid:3) Stability of Relative Equilibrium..............................................22
1.3.4(cid:3) Attitude Motion of a Gyrostat...................................................26
1.4(cid:3) Attitude Motion of Torque-free Spacecraft...........................................27
1.4.1(cid:3) Torque-free Rigid Body............................................................27
1.4.2(cid:3) Torque-free Gyrostat.................................................................29
1.4.3(cid:3) Influence of Energy Dissipation on Spinning Spacecraft.........31
References.....................................................................................................32

Chapter 2(cid:3) A Survey of Chaos Theory............................................................33
2.1(cid:3) The Overview of Chaos........................................................................34
2.1.1(cid:3) Descriptions of Chaos...............................................................34
2.1.2(cid:3) Geometrical Structures of Chaos..............................................35
2.1.3(cid:3) Routes to Chaos........................................................................37
2.2(cid:3) Numerical Identification of Chaos........................................................40
2.2.1(cid:3) Introduction...............................................................................40
2.2.2(cid:3) Lyapunov Exponents.................................................................40
2.2.3(cid:3) Power Spectra...........................................................................42
2.3(cid:3) Melnikov Theory..................................................................................44
2.3.1(cid:3) Introduction...............................................................................44
2.3.2(cid:3) Transversal Homoclinic/Heteroclinic Point..............................44