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E-grāmata: Chaos in Attitude Dynamics of Spacecraft

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  • Formāts: PDF+DRM
  • Izdošanas datums: 13-Apr-2013
  • Izdevniecība: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • Valoda: eng
  • ISBN-13: 9783642300806
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Chaos in Attitude Dynamics of SpacecraftPalielināt
  • Formāts: PDF+DRM
  • Izdošanas datums: 13-Apr-2013
  • Izdevniecība: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • Valoda: eng
  • ISBN-13: 9783642300806
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Attitude dynamics is the theoretical basis of attitude control of spacecrafts in aerospace engineering. With the development of nonlinear dynamics, chaos in spacecraft attitude dynamics has drawn great attention since the 1990's. The problem of the predictability and controllability of the chaotic attitude motion of a spacecraft has a practical significance in astronautic science. This 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 well as new mathematical 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.

Chapter 1 Primer on Spacecraft Dynamics
1(32)
1.1 Orbital Motion of Spacecraft
2(10)
1.1.1 Gravitational Field of a Particle
2(1)
1.1.2 Gravitational Field of a Rigid Body
2(2)
1.1.3 Dynamical Equations of Two-body System
4(1)
1.1.4 First Integrals
5(3)
1.1.5 Characteristics of Keplerian Orbit
8(2)
1.1.6 Elliptic Orbit
10(2)
1.2 Environmental Torques Acting on Spacecraft
12(5)
1.2.1 Gravitational Torque
12(3)
1.2.2 Magnetic Torque
15(2)
1.3 Attitude Motion of Spacecraft in the Gravitational Field
17(10)
1.3.1 Euler's Equations and Poisson's Equations
17(2)
1.3.2 Planar Libration
19(3)
1.3.3 Stability of Relative Equilibrium
22(4)
1.3.4 Attitude Motion of a Gyrostat
26(1)
1.4 Attitude Motion of Torque-free Spacecraft
27(5)
1.4.1 Torque-free Rigid Body
27(2)
1.4.2 Torque-free Gyrostat
29(2)
1.4.3 Influence of Energy Dissipation on Spinning Spacecraft
31(1)
References
32(1)
Chapter 2 A Survey of Chaos Theory
33(30)
2.1 The Overview of Chaos
34(6)
2.1.1 Descriptions of Chaos
34(1)
2.1.2 Geometrical Structures of Chaos
35(2)
2.1.3 Routes to Chaos
37(3)
2.2 Numerical Identification of Chaos
40(4)
2.2.1 Introduction
40(1)
2.2.2 Lyapunov Exponents
40(2)
2.2.3 Power Spectra
42(2)
2.3 Melnikov Theory
44(7)
2.3.1 Introduction
44(1)
2.3.2 Transversal Homoclinic/Heteroclinic Point
44(3)
2.3.3 Analytical Prediction
47(3)
2.3.4 Interruptions
50(1)
2.4 Chaos in Hamiltonian Systems
51(10)
2.4.1 Hamiltonian Systems, Integrability and KAM Theorem
51(4)
2.4.2 Stochastic Layers and Global Chaos
55(3)
2.4.3 Arnol'd Diffusion
58(1)
2.4.4 Higher-Dimensional Version of Melnikov Theory
59(2)
References
61(2)
Chapter 3 Chaos in Planar Attitude Motion of Spacecraft
63(36)
3.1 Rigid Spacecraft in an Elliptic Orbit
64(5)
3.1.1 Introduction
64(1)
3.1.2 Dynamical Model
65(1)
3.1.3 Melnikov Analysis
66(2)
3.1.4 Numerical Simulations
68(1)
3.2 Tethered Satellite Systems
69(6)
3.2.1 Introduction
69(1)
3.2.2 Dynamical Models
70(3)
3.2.3 Melnikov Analysis of the Uncoupled Case
73(1)
3.2.4 Numerical Simulations
74(1)
3.3 Magnetic Rigid Spacecraft in a Circular Orbit
75(14)
3.3.1 Introduction
75(2)
3.3.2 Dynamical Model
77(2)
3.3.3 Melnikov Analysis
79(1)
3.3.4 Numerical Investigations: Undamped Case
80(3)
3.3.5 Numerical Investigations: Damped Case
83(6)
3.4 Magnetic Rigid Spacecraft in an Elliptic Orbit
89(6)
3.4.1 Introduction
89(1)
3.4.2 Dynamical Model
89(2)
3.4.3 Melnikov Analysis
91(1)
3.4.4 Numerical Simulations
92(3)
References
95(4)
Chapter 4 Chaos in Spatial Attitude Motion of Spacecraft
99(32)
4.1 Attitude Motion Described by Serret-Andoyer Variables
100(8)
4.1.1 Serret-Andoyer Variables
100(3)
4.1.2 Torque-free Rigid Body
103(1)
4.1.3 Torque-free Gyrostat
104(2)
4.1.4 Gyrostat in the Gravitational Field
106(1)
4.1.5 Influence of the Geomagnetic Field
107(1)
4.2 Rigid-body Spacecraft in an Elliptic Orbit
108(5)
4.2.1 Introduction
108(1)
4.2.2 Dynamical Model
109(2)
4.2.3 Melnikov Analysis
111(2)
4.2.4 Numerical Simulations
113(1)
4.3 Rigid-body Spacecraft with an Eccentrically Rotating Mass
113(7)
4.3.1 Introduction
113(3)
4.3.2 Dynamical Model
116(1)
4.3.3 Melnikov Analysis
117(2)
4.3.4 Numerical Simulations
119(1)
4.4 Magnetic Gyrostat Spacecraft in a Circular Orbit
120(7)
4.4.1 Introduction
120(2)
4.4.2 Unperturbed Motion of a Gyrostat
122(1)
4.4.3 Melnikov Analysis
123(2)
4.4.4 Numerical Simulations
125(2)
References
127(4)
Chapter 5 Control of Chaotic Attitude Motion
131
5.1 Control of Chaos: An Overview
131(6)
5.1.1 Introduction
131(2)
5.1.2 Problem Formulations
133(1)
5.1.3 OGY Method and Its Generalization
134(2)
5.1.4 Synchronization: Chaos Control in a Broader Sense
136(1)
5.2 The Parametric Open-plus-closed-loop Method
137(8)
5.2.1 Introduction
137(1)
5.2.2 The Control Law
138(2)
5.2.3 Numerical Examples
140(4)
5.2.4 Discussions
144(1)
5.3 The Stability Criterion Method
145(8)
5.3.1 Introduction
145(1)
5.3.2 The Control Law
146(1)
5.3.3 Numerical Examples
147(6)
5.4 Controlling Chaotic Attitude Motions
153(7)
5.4.1 Introduction
153(1)
5.4.2 Dynamical Model of Controlled Spacecraft
154(1)
5.4.3 Applications of the Parametric Open-plus-closed-loop Method
155(1)
5.4.4 Applications of the Stability Criterion Method
156(4)
References
160
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