航天器姿態(tài)動(dòng)力學(xué)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