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Dedication | |

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Preface | |

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Kinematics | |

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Physical vectors | |

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Scalar Product | |

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Vector Cross Product | |

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Other Useful Vector Identities | |

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Reference Frames and Physical Vector Coordinates | |

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Vector Addition and Scalar Multiplication | |

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Scalar Product | |

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Vector Cross Product | |

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Column Matrix Identities | |

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Rotation Matrices | |

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Principal Rotations | |

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General Rotations | |

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Euler Angles | |

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Quaternions | |

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Derivatives of Vectors | |

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Angular Velocity | |

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Angular Velocity in Terms of Euler Angle Rates | |

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Angular Velocity in Terms of Quaternion Rates | |

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Velocity and Acceleration | |

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More Rigorous Definition of Angular Velocity 35 References 37 2 Rigid Body Dynamics | |

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Dynamics of a Single Particle | |

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Dynamics of a System of Particles | |

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Rigid Body Dynamics | |

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Translational Dynamics | |

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Rotational Dynamics | |

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The Inertia Matrix | |

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A Parallel Axis Theorem | |

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A Rotational Transformation Theorem | |

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Principal Axes | |

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Kinetic Energy of a Rigid Body 51 References 53 3 The Keplerian Two-Body Problem | |

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Equations of motion | |

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Constants of the motion | |

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Orbital Angular Momentum | |

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Orbital Energy | |

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The Eccentricity Vector | |

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Shape of a Keplerian orbit | |

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Perifocal Coordinate System | |

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Kepler's Laws | |

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Time of Flight | |

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Circular Orbits | |

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Elliptical Orbits | |

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Parabolic Orbits | |

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Hyperbolic Orbits | |

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Orbital Elements | |

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Heliocentric-Ecliptic Coordinate System | |

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Geocentric-Equatorial Coordinate System | |

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Orbital Elements given Position and Velocity | |

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Position and Velocity given Orbital Elements 80 References 84 4 Preliminary Orbit Determination | |

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Orbit Determination from Three Position Vectors | |

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Orbit Determination from Three Line-of-Sight Vectors | |

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Orbit Determination from Two Position Vectors and Time (Lambert's Problem) | |

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The Lagrangian Coefficients 94 References 98 5 Orbital Maneuvers | |

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Simple ImpulsiveManeuvers | |

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Coplanar Maneuvers | |

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Hohmann Transfers | |

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Bi-Elliptic Transfers | |

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Plane Change Maneuvers | |

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Combined Maneuvers | |

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Rendezvous 110 References 111 6 Interplanetary Trajectories | |

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Sphere of Influence | |

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Interplanetary Hohmann Transfers | |

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Patched Conics | |

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Departure Hyperbola | |

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Arrival Hyperbola | |

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Planetary Flyby | |

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Planetary Capture 127 References 129 7 Orbital Perturbations | |

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Special Perturbations | |

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Cowell's Method | |

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Encke's Method | |

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General Perturbations | |

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Gravitational Perturbations due to a Non-Spherical Primary Body | |

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The Perturbative Force Per Unit Mass Due to J2 | |

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Effect of J2 on the orbital elements | |

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Special Types of Orbits | |

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Sun-synchronous orbits | |

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Molniya Orbits | |

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Small Impulse Form of the Gauss Variational Equations | |

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Derivation of the Remaining Gauss Variational Equations 149 References 156 8 Low Thrust Trajectory Analysis and Design | |

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Problem Formulation | |

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Coplanar Circle to Circle Transfers | |

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Plane Change Maneuver 160 References 161 9 Spacecraft Formation Flying | |

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Mathematical Description | |

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Relative Motion Solutions | |

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Out-of-PlaneMotion | |

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In-Plane Motion | |

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Alternative Description for In-Plane Relative Motion | |

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Further Examination of In-Plane Motion | |

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Out-of-PlaneMotion - Revisited | |

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Special Types of Relative Orbits | |

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Along-Track Orbits | |

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Projected Elliptical Orbits | |

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Projected Circular Orbits 178 References 178 10 The Restricted Three-Body Problem | |

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Formulation | |

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Equations of Motion | |

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The Lagrangian Points | |

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Case (i) | |

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Case (ii) | |

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Stability of the Lagrangian Points | |

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Comments | |

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Jacobi's Integral | |

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Hill's Curves | |

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Comments on Figure | |

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187 References 187 11 Introduction to Spacecraft Attitude Stabilization | |

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Introduction to Control Systems | |

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Overview of Attitude Representation and Kinematics | |

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Overview of Spacecraft Attitude Dynamics 193 12 Disturbance Torques on a Spacecraft | |

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Magnetic Torque | |

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Solar Radiation Pressure Torque | |

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Aerodynamic Torque | |

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Gravity-Gradient Torque 199 References 202 13 Torque-Free Attitude Motion | |

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Solution for an Axisymmetric Body | |

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Physical Interpretation of the Motion 209 References 212 14 Spin Stabilization | |

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Stability | |

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Spin Stability of Torque-FreeMotion | |

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Effect of Internal Energy Dissipation 217 References 218 15 Dual-Spin Stabilization | |

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Equations of Motion | |

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Stability of Dual-Spin Torque-FreeMotion | |

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Effect of Internal Energy Dissipation 222 References 228 16 Gravity-Gradient Stabilization | |

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Equations of Motion | |

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Stability Analysis | |

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Pitch Motion | |

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Roll-Yaw Motion | |

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Combined Pitch and Roll/Yaw 237 References 238 17 Active Spacecraft Attitude Control | |

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Attitude Control for a Nominally Inertially Fixed Spacecraft | |

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Transfer Function Representation of a System | |

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System Response to an Impulsive Input | |

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Block Diagrams | |

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The Feedback Control Problem | |

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Typical Control Laws | |

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Proportional "P" Control | |

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Proportional Derivative "PD" Control | |

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Proportional Integral Derivative "PID" Control | |

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Time-Domain Specifications | |

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Transient Specifications | |

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Factors that Modify the Transient Behavior | |

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Effect of Zeros | |

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Effect of Additional Poles | |

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Steady-State Specifications and System Type | |

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Effect of Disturbances | |

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Actuator Limitations | |

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References | |

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Routh's Stability Criterion | |

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Proportional-Derivative Control with Actuator Dynamics | |

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Active Dual-Spin Stabilization | |

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References | |

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The Root Locus | |

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Rules for Constructing the Root Locus | |

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PD Attitude Control with Actuator Dynamics - Revisited | |

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Derivation of the Rules for Constructing the Root Locus | |

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References | |

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Control Design by the Root Locus Method | |

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Typical Types of Controllers | |

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PID Design for Spacecraft Attitude Control | |

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References | |

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Frequency Response | |

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Frequency Response and Bode Plots | |

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Plotting the Frequency Response as a Function of ï¿½ (Bode Plots) | |

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Low-Pass Filter Design | |

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References | |

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Relative Stability | |

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Polar Plots | |

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Nyquist Stability Criterion | |

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Argument Principle | |

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Stability Analysis of the Closed-Loop System | |

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Stability Margins | |

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Stability Margin Definitions | |

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References | |

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Control Design in the Frequency Domain | |

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Feedback Control Problem - Revisited | |

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Closed-Loop Tracking Error | |

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Closed-Loop Control Effort | |

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Modified Control Implementation | |

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Control Design | |

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Frequency Responses for Common Controllers | |

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Example - PID Design for Spacecraft Attitude Control | |

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References | |

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Nonlinear Spacecraft Attitude Control | |

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State-Space Representation of the Spacecraft Attitude Equations | |

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Stability Definitions | |

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Equilibrium Points | |

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Stability of Equilibria | |

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Stability Analysis | |

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Detumbling of a Rigid Spacecraft | |

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Lyapunov Stability Theorems | |

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LaSalle's Theorem | |

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Spacecraft Attitude Control with Quaternion and Angular Rate Feedback | |

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Controller Gain Selection | |

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References | |

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Spacecraft Navigation | |

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Review of Probability Theory | |

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Continuous Random Variables and Probability Density Functions | |

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Mean and Covariance | |

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Gaussian Probability Density Functions | |

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Discrete-TimeWhite Noise | |

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Simulating Noise | |

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Batch Approaches for Spacecraft Attitude Estimation | |

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Wahba's Problem | |

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Davenport's q-Method | |

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The QUEST Algorithm | |

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The TRIAD Algorithm | |

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Example | |

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The Kalman Filter | |

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The Discrete-Time Kalman Filter | |

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The Norm-Constrained Kalman Filter | |

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Spacecraft Attitude Estimation Using the Norm-Constrained Extended Kalman Filter | |

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References | |

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Practical Spacecraft Attitude Control Design Issues | |

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Attitude Sensors | |

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Sun-Sensors | |

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Three-AxisMagnetometers | |

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Earth Sensors | |

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Star Trackers | |

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Rate Sensors | |

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Attitude Actuators | |

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Thrusters | |

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Magnetic Torquers | |

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ReactionWheels | |

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MomentumWheels | |

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Control Moment Gyroscopes | |

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Control Law Implementation | |

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Time-Domain Representation of a Transfer Function | |

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Control Law Digitization | |

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Closed-Loop Stability Analysis | |

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Sampling Considerations | |

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Unmodeled dynamics | |

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Effects of Spacecraft Flexibility | |

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Effects of Propellant Sloshing | |

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References | |

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Index | |