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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 � (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 | |