Anton de Ruiter, Assistant Professor, Mechanical and Aerospace Engineering Department, Carleton University, Ottawa, Canada.Obtained his PhD in Aerospace Engineering from the University of Toronto in 2005.? Until 2006 he was a Visiting Research Fellow at the Space Technologies Branch of the Canadian Space Agency.?His interests include Nano-Satellite Technologies, Interplanetary Missions, Spacecraft Formation Flying, Spacecraft Attitude and Orbit Determination and Control, GPS-based Spacecraft Navigation, Control Systems, and Optimization Theory and Applications.?Professor De Ruiter has written extensively on spacecraft dynamics and related topics for journals, articled papers and conference proceedings. Christopher J. Damaren, Professor, University of Toronto Institute for Aerospace Studies.Obtained his doctorate at UTIAS in 1990 in the area of control systems for flexible spacecraft. In the 1990's most of his research concentrated on control system design for large structurally flexible robot manipulator systems such as the Space Station robotic systems developed by Canada. Since joining the faculty of UTIAS in 1999, his research group has been involved in the dynamics and control of spacecraft including the orbital, attitude, and structural motions of these systems. James R. Forbes, Assistant Professor, Department of Mechanical Engineering, McGill University.Obtained his doctorate at UTIAS in 2011 in the area of control system design with applications to aerospace systems, including spacecraft attitude control. His teaching duties at McGill University include spacecraft dynamics and control courses at the upper undergraduate/beginning graduate level

• Preface xvii1 Kinematics 11.1 Physical Vectors 11.2 Reference Frames and Physical Vector Coordinates 61.3 Rotation Matrices 111.4 Derivatives of Vectors 321.5 Velocity and Acceleration 411.6 More Rigorous Definition of Angular Velocity 42Notes 44References 452 Rigid Body Dynamics 472.1 Dynamics of a Single Particle 472.2 Dynamics of a System of Particles 492.3 Rigid Body Dynamics 522.4 The Inertia Matrix 562.5 Kinetic Energy of a Rigid Body 60Notes 63References 633 The Keplerian Two-Body Problem 653.1 Equations of Motion 653.2 Constants of the Motion 673.3 Shape of a Keplerian Orbit 693.4 Kepler’s Laws 803.5 Time of Flight 833.6 Orbital Elements 893.7 Orbital Elements given Position and Velocity 923.8 Position and Velocity given Orbital Elements 94Notes 98References 984 Preliminary Orbit Determination 994.1 Orbit Determination from Three Position Vectors 994.2 Orbit Determination from Three Line-of-Sight Vectors 1034.3 Orbit Determination from Two Position Vectors and Time (Lambert’s Problem) 109Notes 114References 1145 Orbital Maneuvers 1155.1 Simple Impulsive Maneuvers 1155.2 Coplanar Maneuvers 1165.3 Plane Change Maneuvers 1235.4 Combined Maneuvers 1255.5 Rendezvous 127Notes 128Reference 1286 Interplanetary Trajectories 1296.1 Sphere of Influence 1296.2 Interplanetary Hohmann Transfers 1336.3 Patched Conics 1376.4 Planetary Flyby 1436.5 Planetary Capture 145Notes 146References 1477 Orbital Perturbations 1497.1 Special Perturbations 1507.1.1 Cowell’s Method 1517.2 General Perturbations 1547.3 Gravitational Perturbations due to a Non-Spherical Primary Body 1567.4 Effect of J2 on the Orbital Elements 1647.5 Special Types of Orbits 1687.6 Small Impulse Form of the Gauss Variational Equations 1697.7 Derivation of the Remaining Gauss Variational Equations 171Notes 180References 1818 Low Thrust Trajectory Analysis and Design 1838.1 Problem Formulation 1838.2 Coplanar Circle to Circle Transfers 1848.3 Plane Change Maneuver 186Notes 188References 1889 Spacecraft Formation Flying 1899.1 Mathematical Description 1909.2 Relative Motion Solutions 1949.3 Special Types of Relative Orbits 203Notes 207Reference 20710 The Restricted Three-Body Problem 20910.1 Formulation 20910.2 The Lagrangian Points 21210.3 Stability of the Lagrangian Points 21410.4 Jacobi’s Integral 215Notes 218References 21811 Introduction to Spacecraft Attitude Stabilization 21911.1 Introduction to Control Systems 22011.2 Overview of Attitude Representation and Kinematics 22211.3 Overview of Spacecraft Attitude Dynamics 22312 Disturbance Torques on a Spacecraft 22712.1 Magnetic Torque 22712.2 Solar Radiation Pressure Torque 22812.3 Aerodynamic Torque 23012.4 Gravity-Gradient Torque 231Notes 234Reference 23413 Torque-Free Attitude Motion 23513.1 Solution for an Axisymmetric Body 23513.2 Physical Interpretation of the Motion 242Notes 245References 24514 Spin Stabilization 24714.1 Stability 24714.2 Spin Stability of Torque-Free Motion 24914.3 Effect of Internal Energy Dissipation 252Notes 253References 25315 Dual-Spin Stabilization 25515.1 Equations of Motion 25515.2 Stability of Dual-Spin Torque-Free Motion 25715.3 Effect of Internal Energy Dissipation 259Notes 266References 26616 Gravity-Gradient Stabilization 26716.1 Equations of Motion 26816.2 Stability Analysis 272Notes 277References 27717 Active Spacecraft Attitude Control 27917.1 Attitude Control for a Nominally Inertially Fixed Spacecraft 28017.2 Transfer Function Representation of a System 28117.3 System Response to an Impulsive Input 28217.4 Block Diagrams 28417.5 The Feedback Control Problem 28617.6 Typical Control Laws 28917.7 Time-Domain Specifications 29217.8 Factors that Modify the Transient Behavior 30817.9 Steady-State Specifications and System Type 311                      JWST251-FM JWST251-De-Ruiter Printer: Yet to Come November 2, 2012 14:18 Trim: 244mm×168mmviiiContents2.4 The Inertia Matrix 562.4.1 A Parallel Axis Theorem572.4.2 A Rotational Transformation Theorem582.4.3 Principal Axes592.5 Kinetic Energy of a Rigid Body 60Notes63References 633 The Keplerian Two-Body Problem 653.1 Equations of Motion 653.2 Constants of the Motion 673.2.1 Orbital Angular Momentum673.2.2 Orbital Energy673.2.3 The Eccentricity Vector683.3 Shape of a Keplerian Orbit 693.3.1 Perifocal Coordinate System723.4 Kepler’s Laws 803.5 Time of Flight 833.5.1 Circular Orbits833.5.2 Elliptical Orbits843.5.3 Parabolic Orbits883.5.4 Hyperbolic Orbits893.6 Orbital Elements 893.6.1 Heliocentric-Ecliptic Coordinate System893.6.2 Geocentric-Equatorial Coordinate System903.7 Orbital Elements given Position and Velocity 923.8 Position and Velocity given Orbital Elements 94Notes98References 984 Preliminary Orbit Determination 994.1 Orbit Determination from Three Position Vectors 994.2 Orbit Determination from Three Line-of-Sight Vectors 1034.3 Orbit Determination from Two Position Vectors and Time (Lambert’sProblem) 1094.3.1 The Lagrangian Coefficients110Notes114References 1145 Orbital Maneuvers 1155.1 Simple Impulsive Maneuvers 1155.2 Coplanar Maneuvers 1165.2.1 Hohmann Transfers1185.2.2 Bi-Elliptic Transfers1205.3 Plane Change Maneuvers 123FOR SCREEN VIEWING IN DART ONLYJWST251-FM JWST251-De-Ruiter Printer: Yet to Come November 2, 2012 14:18 Trim: 244mm×168mmContentsix5.4 Combined Maneuvers 1255.5 Rendezvous 127Notes128Reference 1286 Interplanetary Trajectories 1296.1 Sphere of Influence 1296.2 Interplanetary Hohmann Transfers 1336.3 Patched Conics 1376.3.1 Departure Hyperbola1396.3.2 Arrival Hyperbola1416.4 Planetary Flyby 1436.5 Planetary Capture 145Notes146References 1477 Orbital Perturbations 1497.1 Special Perturbations 1507.1.1 Cowell’s Method1517.1.2 Encke’s Method1517.2 General Perturbations 1547.3 Gravitational Perturbations due to a Non-Spherical Primary Body 1567.3.1 The Perturbative Force Per Unit Mass Due to J21637.4 Effect ofJ2on the Orbital Elements 1647.5 Special Types of Orbits 1687.5.1 Sun-Synchronous Orbits1687.5.2 Molniya Orbits1697.6 Small Impulse Form of the Gauss Variational Equations 1697.7 Derivation of the Remaining Gauss Variational Equations 171Notes180References 1818 Low Thrust Trajectory Analysis and Design 1838.1 Problem Formulation 1838.2 Coplanar Circle to Circle Transfers 1848.3 Plane Change Maneuver 186Notes188References 1889 Spacecraft Formation Flying 1899.1 Mathematical Description 1909.2 Relative Motion Solutions 1949.2.1 Out-of-Plane Motion1959.2.2 In-Plane Motion195FOR SCREEN VIEWING IN DART ONLYJWST251-FM JWST251-De-Ruiter Printer: Yet to Come November 2, 2012 14:18 Trim: 244mm×168mmxContents9.2.3 Alternative Description for In-Plane Relative Motion1989.2.4 Further Examination of In-Plane Motion2009.2.5 Out-of-Plane Motion - Revisited2029.3 Special Types of Relative Orbits 2039.3.1 Along-Track Orbits2039.3.2 Projected Elliptical Orbits2049.3.3 Projected Circular Orbits207Notes207Reference 20710 The Restricted Three-Body Problem 20910.1 Formulation 20910.1.1 Equations of Motion21110.2 The Lagrangian Points 21210.2.1 Case (i)21210.2.2 Case (ii)21310.3 Stability of the Lagrangian Points 21410.3.1 Comments21510.4 Jacobi’s Integral 21510.4.1 Hill’s Curves21610.4.2 Comments on Figure 10.5218Notes218References 21811 Introduction to Spacecraft Attitude Stabilization 21911.1 Introduction to Control Systems 22011.1.1 Open-loop versus Closed-loop22011.1.2 Typical Feedback Control Structure22111.2 Overview of Attitude Representation and Kinematics 22211.3 Overview of Spacecraft Attitude Dynamics 22311.3.1 Properties of the Inertia Matrix - A Summary22412 Disturbance Torques on a Spacecraft 22712.1 Magnetic Torque 22712.2 Solar Radiation Pressure Torque 22812.3 Aerodynamic Torque 23012.4 Gravity-Gradient Torque 231Notes234Reference 23413 Torque-Free Attitude Motion 23513.1 Solution for an Axisymmetric Body 23513.2 Physical Interpretation of the Motion 242Notes245References 245FOR SCREEN VIEWING IN DART ONLYJWST251-FM JWST251-De-Ruiter Printer: Yet to Come November 2, 2012 14:18 Trim: 244mm×168mmContentsxi14 Spin Stabilization 24714.1 Stability 24714.2 Spin Stability of Torque-Free Motion 24914.3 Effect of Internal Energy Dissipation 25214.3.1 Energy Sink Hypothesis25214.3.2 Major Axis Rule253Notes253References 25315 Dual-Spin Stabilization 25515.1 Equations of Motion 25515.2 Stability of Dual-Spin Torque-Free Motion 25715.3 Effect of Internal Energy Dissipation 259Notes266References 26616 Gravity-Gradient Stabilization 26716.1 Equations of Motion 26816.2 Stability Analysis 27216.2.1 Pitch Motion27216.2.2 Roll-Yaw Motion27316.2.3 Combined Pitch and Roll/Yaw277Notes277References 27717 Active Spacecraft Attitude Control 27917.1 Attitude Control for a Nominally Inertially Fixed Spacecraft 28017.2 Transfer Function Representation of a System 28117.3 System Response to an Impulsive Input 28217.4 Block Diagrams 28417.5 The Feedback Control Problem 28617.6 Typical Control Laws 28917.7 Time-Domain Specifications 29217.8 Factors that Modify the Transient Behavior 30817.9 Steady-State Specifications and System Type 31117.10 Effect of Disturbances 31617.11 Actuator Limitations 319Notes 320References 32018 Routh’s Stability Criterion 32118.1 Proportional-Derivative Control with Actuator Dynamics 32218.2 Active Dual-Spin Stabilization 325Notes 330References 33019 The Root Locus 33119.1 Rules for Constructing the Root Locus 33219.2 PD Attitude Control with Actuator Dynamics - Revisited 34119.3 Derivation of the Rules for Constructing the Root Locus 345Notes 353References 35320 Control Design by the Root Locus Method 35520.1 Typical Types of Controllers 35720.2 PID Design for Spacecraft Attitude Control 361Notes 369References 36921 Frequency Response 37121.1 Frequency Response and Bode Plots 37221.2 Low-Pass Filter Design 383Notes 385References 38522 Relative Stability 38722.1 Polar Plots 38722.2 Nyquist Stability Criterion 39022.3 Stability Margins 399Notes 410References 41023 Control Design in the Frequency Domain 41123.1 Feedback Control Problem - Revisited 41623.2 Control Design 42223.3 Example - PID Design for Spacecraft Attitude Control 430Notes 435References 43524 Nonlinear Spacecraft Attitude Control 43724.1 State-Space Representation of the Spacecraft Attitude Equations 43724.2 Stability Definitions 44024.3 Stability Analysis 44224.4 LaSalle’s Theorem 44824.5 Spacecraft Attitude Control with Quaternion and Angular Rate Feedback 451Notes 456References 45725 Spacecraft Navigation 45925.1 Review of Probability Theory 45925.2 Batch Approaches for Spacecraft Attitude Estimation 46725.3 The Kalman Filter 477Notes 496References 49726 Practical Spacecraft Attitude Control Design Issues 49926.1 Attitude Sensors 49926.2 Attitude Actuators 50626.3 Control Law Implementation 51126.4 Unmodeled Dynamics 523Notes 539ReferencesAppendix A: Review of Complex Variables 541Appendix B: Numerical Simulation of Spacecraft Motion 557Notes 561Reference 561Index 563

“In conclusion, this book covers a broad range of areas – including some more in-depth content (stabilisation techniques, practical design issues) – and is best used as an introductory text to the field for latter year undergraduates.”  (The Aeronautical Journal, 1 November 2014)“Overall, this book provides a good, comprehensive examination of the fundamentals of translational and rotational dynamics, determination, and control of spacecraft.  Summing Up: Recommended.  All academic and professional aerospace engineering collections.”  (Choice, 1 September 2013)