编队和集群飞行:动力学、控制和设计

Chapter 1 Introduction
Chapter 2 Bounded Relative Orbits in the Zonal Gravitational Field
2.1 Introduction
2.2 Equations of Relative Motion Under Higher-Order Zonal Harmonic Perturbations
2.3 Bounded Relative Orbits Constraints
2.4 Bounded Relative Quasi-Periodic Orbits by the Multiple-Shooting Approach
2.5 Conclusions
Chapter 3 J2 Invariant Relative Orbits via Differential Correction Algorithm
3.1 Introduction
3.2 Hamiltonian Model for Relative Motion Dynamics
3.2.1 Coordinate Definition
3.2.2 J2 Absolute Dynamics
3.2.3 J2 Relative Dynamics
3.2.4 Perturbed Period
3.3 Existence and Denseness of Invariant Orbit
3.3.1 Existence
3.3.2 Denseness
3.4 Differential Correction
3.4.1 Correction Algorithm
3.4.2 Convergency
3.4.3 Numerical Simulation
3.5 Period and Stability of Invariant Orbit
3.5.1 Period of Invariant Orbit
3.5.2 Stable and Unstable Manifolds
3.6 Compatibility between J2 Invariant Orbit and Formation Configuration
3.6.1 Formation Configuration
3.6.2 Compatibility Definition
3.6.3 Numerical Simulation
3.7 Influences of Measure Errors on Correction
3.7.1 Dispersion Error Analysis
3.7.2 Monte Carlo Simulation
3.8 Conclusions
Chapter 4 On the Existence of J2 Invariant Relative Orbits from the Dynamical System Point of View
4.1 Introduction
4.2 J2 Hamiltonian Dynamics from Dynamical System Point of View
4.2.1 Coordinate Systems and Variables
4.2.2 Reduced Dynamics
4.2.3 PoincarE Section
4.3 Fixed Point and Its Invariant Manifolds
4.3.1 Location of the Fixed Point
4.3.2 Central Manifolds
4.4 J2 Invariant Relative Obits Generated from Fixed Points and Invariant Manifolds
4.4.1 Definition of J2 Invariant Relative Orbits
4.4.2 J2 Invariant Relative Orbits Generated from Invariant Manifolds
4.4.3 Frequency Analysis on J2 Invariant Relative Orbits
4.5 Conclusions
Chapter 5 Jn Bounded Relative Orbits Design via High-Order Poincare Maps
5.1 Introduction
5.2 Reduced Orbital Dynamics of the Zonal Problem
5.3 Differential Algebra Techniques
5.3.1 The Framework of Differential Algebra
5.3.2 High-Order Expansion of the Flow of an ODE
5.4 Family of Fixed Points Under Higher-Order Zonal Harmonic Perturbations
5.4.1 The General Algorithm to Identify Fixed Point
5.4.2 Family of Fixed Points Parametrized by E and H
5.4.3 Validation of DA Approach
5.4.4 Effects of Order of Zonal Harmonic Perturbations on the Fixed Points
5.5 Design of Long-Term Bounded Relative Orbits
5.5.1 Constraints for Bounded Relative Orbits
5.5.2 High-Order Poincare Maps
5.5.3 Generation of Bounded Relative Motion
5.6 Conclusions
Chapter 6 The J2 Invariant Relative Configuration of Spaeeborne SAR Interferometer for Digital Elevation Measurement
6.1 Introduction
6.2 Digital Elevation Model and Height Measurement Accuracy
6.2.1 InSAR Geometry for Digital Elevation Model
6.2.2 Absolute and Relative Height Measurement Accuracy
6.3 Optimal Baseline Design for Digital Elevation Model
6.4 J2 Invariant Configuration Created by Differential Correction Algorithm
6.4.1 Correction Algorithm
6.4.2 Compatibility Between Invariant Orbits and Formation Configuration
6.5 J2 Invariant Configuration Generated from Optimization
6.6 Conclusions
Chapter 7 Distance-Based Relative Orbital Elements Determination for Formation Flying System
7.1 Introduction
7.2 Problem Formulation and Approximation
7.2.1 Definition of Relative Orbital Elements Differences
7.2.2 Equation of Relative Motion and Its Simplification
7.2.3 Relative Orbital Elements Determination
7.3 Numerical Simulations and Performance Assessment
7.3.1 Numerical Simulations
7.3.2 Performance Assessment
7.4 Conclusions
Chapter 8 Application of Hamiltonian Structure-Preserving Control to Formation Flying on a J 2-Perturbed Mean Circular
Orbit
8.1 Introduction
8.2 Nonlinear Dynamics of Formation Flying
8.2.1 Development of Linearized Different Equation
8.2.2 Numerical Simulations
8.3 Application of Hamiltonian Structure-Preserving Control to Formation Flying about a Mean Circular Orbit
8.3.1 Structure-Preserving Stabilization for Time-Independent Hamiltonian System
8.3.2 Application of Hamiltonian Structure-Preserving Control to Stabilize Relative Motions about a Mean Circular Orbit
8.3.3 Numerical Simulations
8.4 Conclusions
Chapter 9 Wave-Like Patterns in Precessing Elliptical Rings for Swarming Systems
9.1 Introduction
9.2 Orbital Evolution Models of Precessing Elliptical Rings
9.2.1 Precessing Elliptical Orbit Perturbed by J2 and J
9.2.2 Precessing Elliptical Orbit Perturbed by J2 and SRP
9.3 Continuum Models of Number Density for Precessing Elliptical Rings
9.3.1 Continuity Equation Modelled for J2 and SRP Perturbations
9.3.2 Continuity Equation Modelled for J2 and J3 Perturbations
9.3.3 Comparison between Analytic and Numerical Number Density Evolutions
9.4 Applications of Continuum Density Models
9.4.1 Number of Swarm Devices with Distant Apogees for J2 and SRP Perturbations
9.4.2 Number of Satellites Visible Above the Horizon for the J2 and Ja Perturbations
9.5 Conclusions
Chapter 10 Closed-Loop Control of the Orbit Evolution of "Smart Dust" Swarms
10.1 Introduction
10.2 Continuum Evolution Model of Swarm Density
10.3 Control Strategies for the Evolution of Swarm Density
10.3.1 Open-Loop and Closed-Loop Device Controllers for a Homogeneous Continuity Equation
10.3.2 Boundary Control for On-Orbit Failures
10.4 Numerical Simulations
10.5 Conclusions
Appendix A
Appendix B
Appendix C
References

The aim of this book is to introduce the novel approaches for the study ofrelative dynamics modelling, control, and design of formation and swarm flying.Broad research focuses of current interest are covered, with each chapter involvedin different topics. The contents of this book include the introduction, definition,and property of orbital mechanics and control system in the framework offormation and swarm flying concepts using various theoretical methods andnumerical simulations, which have potential merits in mission analysis and design. The book is intended for researchers, teachers, and students of the universitiesand institutes in astrodynamics, control, and interdisciplinary space technologyfields for the purpose of academic study and engineering application.

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