From its roots in classical mechanics and reliance on stability theory to the evolution of practical stabilization ideas, this volume covers environmental torques encountered in space; energy dissipation; motion equations for four archetypical systems; orientation parameters; illustrations of key coCopyrighted materialsCopyright@2004DoverPublicationsRetrievedfromwww.knovel.comPREFACE TO THE DOVEREDITIONWhen i revisited the preface written for the original edition of this book, i wasstruck by how much has changed in this as in so many other technical fields overthe past two decades. At the same time, much also remains fundamentalFortunately, this reference/textbook was written to emphasize the latter. Newcohorts of engineering science students each year encounter the problem of howto design a spacecraft so that it points in the intended direction. And seasonedprofessionals who understand for their own satellite projects, several levels ofdetail beyond what could or should ever be in any single book, occasionally reconsider the fundamentals"for seminal insight, or for some nugget of understand-ing that may spark an innovation. It is my fervent hope that this Dover edition ofspacecraft Attitude Dynamics will assist these helpful processes to continueGeneral RemarksWhen the first artificial satellites were inserted into orbit in the late 1950s theword"artificial"being a legal technicality required to recognize the billion-yearseniority of our natural moon-Sputnik I just tumbled slowly in orbit, andExplorer l, after a brave but ill-fated attempt at spin stabilization, ending up doinga similar slow wobble. Upon these shaky beginnings, a highly successful body ofengineering practice has been built: stringent three-axis control of satellite orientation (not to mention similarly strict requirements for articulated appendages)isnow commonplace. Indeed, no modern space vehicle, whether a low-orbitresources satellite, a geostationary communications platform, an interplanetaryprobe, or any other man-made space apparatus, can accomplish its mission objectives without a properly functioning attitude stabilization and control systemThe Explorer and sputnik experiences sparked a reexamination of the(assumed )implications of the classical analyses of Newton, Euler, and Lagranget is noteworthy that, long after the most egregious implications of the purelyrigid-body version of classical mechanics were proved erroneous, many scores ofstudents were still assaulted with the pre space-age version of the subjectPerhaps, in some places, they still are.All techniques of spacecraft attitude stabilization rest on the twin disciplinesf dynamics and control, as adapted to the special problem of regulating the oriPREFACE TO THE DOVER EDITIONentation of relatively small but very precious hardware packages that must functionfor long periods of time, faultlessly, far beyond reach. This book is about attitudedynamics. The ever-contiguous issues of orbital dynamics, orbital control, and atti-tude control (what attitude dynamics insiders used to call"active"attitude controlare also addressed herein, but only to the extent that they interact with attitudedynamicsTarget Readershave written this book in the first instance, for students, especially those whoare comfortable with vector dynamics and linear algebra. Those committed to adeeper study of the subject will benefit from the 175 problems posed (end of chapters). These are not simply exercises; they usually contain important extensions tothe analysis.I have also tried to incorporate the interests of practicing aerospace engineers,who deserve credit for making this subject more than just a collection of dynamicsanalyses. For them, this work should provide a handy reference book with a coherent exposition in a unified notation. Readers interested in the operational application of the most basic attitude stabilization ideas will especially appreciate the historical"experiments"related in Chapters 9, 10, and ll. One should never wandertoo far based on analysis aloneI was also mindful of those who, through their research endeavors, continue toexpand the theoretical foundations of the discipline. Whether in universities, government labs, or corporations, i hope they find this book to be an attractive reference work. The 350 references cited (up to 1986) should lead to further researchideas. Teachers should find the problems at the end of each chapter a helpfulresourceA Quick Look at ContentsAfter an introductory chapter to set the context, Chapters 2 and 3 provide kine-matical and dynamical fundamentals. Chapter 4 then examines a classical subjectthe torque-free motion of a rigid body--from a modern viewpoint and chapter 5treats the all-important subject of how energy dissipation affects the attitude stability of spinning bodies. Chapters 6 and 7, the last of the"torque-free motion "chapters, do for dual-spin systems(systems that include one or more spinning wheels orrotors)what Chapters 4 and 5 do for monospinners.Among the most characteristic features of spacecraft attitude dynamics are thesubtle traits caused by the small environmental torq ues encountered in space. eventhough weak by conventional standards, their cumulative effect can be pronouncedChapter 8 is set aside for a discussion of this topic. It includes a detailed examination of gravitational, aerodynamic, and solar-radiation pressure torquesThe ultimate objective of the book to explicate the dynamics underlying spacecraft attitude stabilization systemsis then encountered in Chapters 9, 10, and llThey are concerned with gravity-gradient stabilization, spin stabilization, and dualspin stabilization(either external rotors or internal momentum wheels), and includeon-orbit ex periencePREFACE TO THE DOVER EDITIONFunding AcknowledgementsFinancial support for this book was provided by the university of TorontoInstitute for Aerospace Studies(UTIAS) and by the Natural Sciences andEngineering Research Council (NSERC)Personal AcknowledgementsFinally, and with pleasure, my personal acknowledgements. My academic jour-ney has witnessed four UTIAS Directors-Gordon Patterson, Jaap de leeuwRod Tennyson, and Tony Haasz and all have enabled and encouraged me to pursue this and other research initiatives. grant Harrington was helpful in examiningthe books contextual evaluationIda abert created all the figures at a time when less technology was availableand more artistic ability was required my best thanks to professor chris hall ofthe aerospace and ocean engineering department at Virginia Tech for his continued interest in this book, as best evidenced by his help with making the matchbetween Dover and myself in general, and with John Grafton in particular.I learned most from my students(including 48 M. A Sc and 33 Ph. D candi-dates). Working with all these bright, creative individuals endures for me as thegreatest pleasure of my professional experienceLast, and most important, my abiding thanks to my wife, Joanne, whose experttyping of the original manuscript was but the most tangible expression of herunflagging support while I wrote this bookCopyrighted materialsCopyright@2004DoverPublicationsRetrievedfromwww.knovel.comCONTENTSCHAPTER 1 INTRODUCTIONCHAPTER 2 ROTATIONAL KINEMATICS回回2.1 Relerence frames and rotations2.2 Angular Displacement Parameters152.3 Angular Velocity222.4 Comments on Parameter Alternatives25 ProblemsCHAPTER 3 ATTITUDE MOTION EQUATIONS3.1 Motion Equations for a Point Mass, gp403.2 Motion Equations for a System of Point Masses, 2gp423.3 Motion Equations for a RIgid Body, si553.4 A System with Damping, gi+ g3.5 A Dual-SpIn System, 9+ yr653. 6 A Simple Multi-Rigid-Body System, ,1t 23.7 Dynamics of a System of Rigid Bodies3. 8 Problems83xc。 NENTSCHAPTER 4 ATTITUDE DYNAMICS OF A RIGID BODY934.1 Basic Motion Equations934.2 Torque-Free Motlon; g Inertially Axisymmetrical4.3 Torque-Free Motion; g Tri-inertial1044.4 Stability of Motion for g1144.5 Motlon of a Rigld Body Under Torque1244, 6 Problems129CHAPTER 5 EFFECT OF INTERNALENERGY DISSIPATION ON THEDIRECTIONAL STABILITY OF SPINNING BODIES1395.1 Quasi-Rigid Body with an Energy Sink, 25.2 Rigld Body with a Point Mass Damper, 9+ gp153 Probles152CHAPTER 6 DIRECTIONAL STABILITYOF MULTISPIN VEHICLES1566.1 The ge+ y Gyrostat1566.2 Gyrostat with Nonspinning Carrier1616.3 The Zero Momentum Gyrostat1G46.4 The General Case1656.5 System of Coaxial wheels1786.6 Problems184CHAPTER 7 EFFECT OF INTERNALENERGY DISSIPATION ON THEDIRECTIONAL STABILITY OF GYROSTATS1927.1 Energy Sink Analyses1937.2 Gyrostats with Discrete Dampers2177.3 Problems225cNTE№SCHAPTER 8 SPACECRAFT TORQUES2328.1 Gravitational Torque2338.2 Aerodynamic Torque2488.3 Radiation Torques2G08. 4 Other Environmental Torques268.5 Nonenvironmental Torques2698.6 Closing Remarks8.7 Problems72CHAPTER 9 GRAVITATIONAL STABILIZATION2B19.1 Contey29.2 Equilibria for a Rigid Body in a Circular Orbit2939.3 DesIgn of Gravitationally stabilized Satellites3139. 4 Flight Experience3359.5 Problems4634CHAPTER 10 SPIN STABILIZATION IN ORBIT10.1 Spinning Rigid Body in Orbit35610.2 Design of Spin-Stabilized Satellites38110.3 Long-Term Efects ofEnvironmental Torques, and Flight Data40010.4 Problems416CHAPTER 11 DUAL-STABILIZATION IN ORBITGYROSTATS AND BIAS MOMENTUM SATELLITES 42311.1 The Gyrostat in Orbit42411.2 Gyrostats with External Rotors44411.3 Bias Momentum Satellites45511. 4 Problems470oEAPPENDIX A ELEMENTS OF STABILITY THEORY480A1 Stabillty Definitions481A2 Stablity of the Origin492A. 3 The LInear Approximation493A4 NonlInear Inferences tromInfinitesimal Stabllity Properties502A.5 Llapunov's Method504A6 Stabllity of LInear Stationary Mechanical Systems510A7 Stabllity Ideas Speciallzed to Attitude Dynamics20APPENDIX B VECTRICES522B.1 Remarks on TermInology523B 2 Vectrlces523B. 3 Several Reference Frames527B 4 KInematics of Vectrices530B5 Derivative with Respect to a vector53APPENDIX C LIST OF SYMBOLS35C1 Lowercase Symbols535C2 Uppercase Symbols535C 3 Lowercase Greek Symbols538C4 Uppercase Greek Symbols539C 5 Other Notational Conventions539REFERENCES541ERRATA559INDEX565Copyrighted materialsCopyright@2004DoverPublicationsRetrievedfromwww.knovel.comCHAPTER 1INTRODUCT ONA spacecraft must point in the right direction. Many satellites are intended tobe Earth oriented; others are intended to face the sun or certain stars of intereststill others are designed to point first at one object, then at another. Often onepart of a spacecraft (a communications antenna perhaps) must point towardEarth, while another part (a solar panel)must face the sun. To achieve suchmission objectives, it is evident that an attitude stabilization and control systemmust be an important part of spacecraft designThe subject of this book is spacecraft attitude dynamics-the applied sciencewhose aim is to understand and predict how spacecraft orientation evolves. as apart of the larger science of dynamics, the book deals with the special problemsassociated with rotational motion, including how to describe the motion(seeChapter 2); how to formulate differential equations that govern the motionChapter 3); and how to make physically meaningful inferences from theseequations( Chapters 4 through 7). And as part of spacecraft technology, it seeksto predict the torques acting on specific spacecraft( Chapter 8)and what attitudemotion these torques will cause, including how to minimize undesirable motionsthrough the application of suitable design strategies(Chapters 9, 10, and 11)Spacecraft attitude dynamics does not, of course, exist in splendid isolation-itnteracts with many other sister disciplines. Indeed, the closer one comes toapplying the principles of spacecraft attitude dynamics to actual spacecraft, themore these interrelationships manifest themselves. Some of the most importantinterfaces are shown in Fig. 1.1Orbit nterfaceIn reality, attitude dynamics (rotational dynamics) and orbital dynamics(translational dynamics) are mutually coupled. (This tends to be less true of