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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

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

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

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.

Intermittency is another frequently observed route to chaos.Intermittency is a phenomenon characterized by random alternations between a regular motion and relatively short irregular bursts.The term intermittency has been used in the theory of turbulence to denote burst of turbulent motion on the background of laminar flow.During early stages of intermittency,for a certain system parameter value,the motion of the system is predominantly periodic with occasional bursts of chaos.As the parameter value is changed,the chaotic bursts become more frequent,andthe time spent in a state of chaos increases and the time spent in periodic motion decreases until,finally,chaos is observed all the time.As a result,the periodic motion becomes chaotic motion. This route was found by Pomeou and Manneville in 1980 [8].Geometrically,the intermittency route is associated with a periodic attractor in the state space bifurcating into a new,larger chaotic attractor,including previous periodic trajectories as its subset.The trajectory of a system can reside some time in the chaotic part of the attractor,but it is ultimately attracted back to the periodic part.As the system parameter is varied,the relative proportion of the chaotic part increases,ultimately covering the whole attractor.
Quasiperiodic torus breakdown is the third typical way that a system may evolve as its parameter is changed. Quasiperiodic torus breakdown route signifies the destruction of the torus and the emergence of a chaotic attractor.The system,if it is not externally driven by a periodic action,may be at equilibrium.As the system parameter is varied,the equilibrium may lose its stability,leading to the emergence of a stable periodic motion.Such a change resulting in a new motion frequency iscalled the Hopf bifurcation.In the state space,a point attractor becomes a periodic attractor.With a further change in the parameter,the periodic attractor undergoes a secondary Hopf bifurcation,resulting in a 2-period quasiperiodic attractor.The trajectories in the state space reside on the surface of a torus.If the two frequencies are incommensurable,the trajectory eventually covers the surface of the torus.For some systems,further changes in the parameter result in the introduction of a third frequency.