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Table of Contents
1 Introduction; 1.1 Background; 1.1.1 Motivations; 1.1.2 Applications; 1.1.3 Challenges; 1.2 Objectives of This Book; 1.3 Preview of Chapters; References; 2 Dynamic Models of Satellite Relative Motion Around an Oblate Earth; 2.1 Introduction; 2.2 Nonlinear Dynamic Model of Relative Motion; 2.2.1 J2 Reference Satellite Dynamics in LVLH Frame; 2.2.1.1 Properties of LVLH Frame; 2.2.1.2 J2 Dynamics of a Satellite in LVLH Frame; 2.2.2 Derivation of Exact J2 Nonlinear Relative Dynamics; 2.2.2.1 Lagrangian Formulation of Relative Motion; 2.2.2.2 Kinetic Energy; 2.2.2.3 Potential Energy.
2.2.2.4 Exact Nonlinear J2 Relative Dynamics2.3 Linearized Dynamic Models of Relative Motion; 2.4 Validation of Proposed Dynamic Models by Simulation; 2.5 Comparison Study of Relative Dynamic Models; 2.5.1 Comparison Method with Model Error Index; 2.5.2 Selected Dynamic Models for Comparison Study; 2.5.2.1 Clohessy-Wiltshire Model; 2.5.2.2 Tschauner-Hempel Model; 2.5.2.3 Unperturbed Nonlinear Model; 2.5.2.4 Schweighart-Sedwick Model; 2.5.2.5 Xu-Wang Model; 2.5.3 Case Studies; 2.5.3.1 Simulation Scenario; 2.5.3.2 Case 1: Error Index Versus Formation Size.
2.5.3.3 Case 2: Error Index Versus Eccentricity2.5.3.4 Case 3: Error Index Versus Inclination; 2.5.3.5 Case 4: Error Index Versus Semimajor Axis; 2.6 Summary; References; 3 Passive and Periodic Satellite Formation Design Around an Oblate Earth; 3.1 Introduction; 3.2 Passive and Periodic Relative Motion Under J2 Perturbation; 3.3 Periodic and Quasi-periodic Relative Orbits at Critical Inclination; 3.3.1 Periodic Relative Orbit; 3.3.2 Quasi-periodic Relative Orbit; 3.3.3 Quasi-periodic Relative Orbit Conditions in Terms of Actual Orbit Variables; 3.3.4 Numerical Simulations.
3.4 In-Plane Satellite Formation in Eccentric Orbits3.4.1 Identical Anomaly In-Plane Formation; 3.4.2 Differential Anomaly In-Plane Formation; 3.4.3 Almost Constant Separation Formation; 3.5 Conclusions; References; 4 Nonlinear Optimization of Low-Thrust Trajectory for Satellite Formation; 4.1 Introduction; 4.2 Nonlinear Relative Motion Dynamics; 4.3 Problem Formulation of Trajectory Optimization for Satellite Formation; 4.3.1 Initial Condition Constraints; 4.3.2 Final Condition Constraints; 4.3.3 Path Constraints; 4.3.4 Linking Constraints; 4.4 Introduction of Legendre Pseudospectral Method.
4.5 Computational Considerations of Nonlinear Programming Problem4.6 Scaling of Nonlinear Programming Problem; 4.6.1 Initial Guess; 4.6.2 Implementation; 4.7 Illustrative Examples; 4.7.1 Example 1: Scenario of Two Satellites, One Burn Phase; 4.7.2 Example 2: Scenario of Two Satellites, Two Phases: Coast-Burn; 4.7.3 Example 3: Scenario of Two Satellites, Three Phases: Burn-Coast-Burn; 4.7.4 Example 4: Scenario of Two Satellites, Four Phases: Coast-Burn-Coast-Burn; 4.7.5 Example 5: Scenario of Formation Reconfiguration Involving Four Satellites.
2.2.2.4 Exact Nonlinear J2 Relative Dynamics2.3 Linearized Dynamic Models of Relative Motion; 2.4 Validation of Proposed Dynamic Models by Simulation; 2.5 Comparison Study of Relative Dynamic Models; 2.5.1 Comparison Method with Model Error Index; 2.5.2 Selected Dynamic Models for Comparison Study; 2.5.2.1 Clohessy-Wiltshire Model; 2.5.2.2 Tschauner-Hempel Model; 2.5.2.3 Unperturbed Nonlinear Model; 2.5.2.4 Schweighart-Sedwick Model; 2.5.2.5 Xu-Wang Model; 2.5.3 Case Studies; 2.5.3.1 Simulation Scenario; 2.5.3.2 Case 1: Error Index Versus Formation Size.
2.5.3.3 Case 2: Error Index Versus Eccentricity2.5.3.4 Case 3: Error Index Versus Inclination; 2.5.3.5 Case 4: Error Index Versus Semimajor Axis; 2.6 Summary; References; 3 Passive and Periodic Satellite Formation Design Around an Oblate Earth; 3.1 Introduction; 3.2 Passive and Periodic Relative Motion Under J2 Perturbation; 3.3 Periodic and Quasi-periodic Relative Orbits at Critical Inclination; 3.3.1 Periodic Relative Orbit; 3.3.2 Quasi-periodic Relative Orbit; 3.3.3 Quasi-periodic Relative Orbit Conditions in Terms of Actual Orbit Variables; 3.3.4 Numerical Simulations.
3.4 In-Plane Satellite Formation in Eccentric Orbits3.4.1 Identical Anomaly In-Plane Formation; 3.4.2 Differential Anomaly In-Plane Formation; 3.4.3 Almost Constant Separation Formation; 3.5 Conclusions; References; 4 Nonlinear Optimization of Low-Thrust Trajectory for Satellite Formation; 4.1 Introduction; 4.2 Nonlinear Relative Motion Dynamics; 4.3 Problem Formulation of Trajectory Optimization for Satellite Formation; 4.3.1 Initial Condition Constraints; 4.3.2 Final Condition Constraints; 4.3.3 Path Constraints; 4.3.4 Linking Constraints; 4.4 Introduction of Legendre Pseudospectral Method.
4.5 Computational Considerations of Nonlinear Programming Problem4.6 Scaling of Nonlinear Programming Problem; 4.6.1 Initial Guess; 4.6.2 Implementation; 4.7 Illustrative Examples; 4.7.1 Example 1: Scenario of Two Satellites, One Burn Phase; 4.7.2 Example 2: Scenario of Two Satellites, Two Phases: Coast-Burn; 4.7.3 Example 3: Scenario of Two Satellites, Three Phases: Burn-Coast-Burn; 4.7.4 Example 4: Scenario of Two Satellites, Four Phases: Coast-Burn-Coast-Burn; 4.7.5 Example 5: Scenario of Formation Reconfiguration Involving Four Satellites.