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SPACECRAFT ATTITUDE DETERMINA TlON AND CONTROL

ASTROPHYSICS AND SPACE SCIENCE LIBRARY VOLUME 73

SPACECRAFT ATTITUDE DETERMINATION AND CONTROL Edited by JAMES R. WERTZ Microcosm, Inc., Torrance ,CA Written by Members of the Technical Staff Attitude Systems Operation Computer Sciences Corporation Preparation of this material was supported by the Attitude Determination and Control Section, Goddard Space Flight Center, National Aeronautics and Space Administration under Contract No. NAS 5-11999 and by the System Sciences Division, Computer Sciences Corporation. KLUWER ACADEMIC PUBLISHERS DORDRECHT f BOSTON f LONDON

library of Congress Cataloging in Publication Data Computer Science Corporation. Attitude Systems Operation. Spacecraft attitude determination and control. (Astrophysics and space science library ; v. 73) 'Contract no. NAS 5-11999.' Bibliography: p. Includes index. 1. Space vehicles-Attitude control systems. 2. Space vehicles-Guidance I. Wertz, James R. systems. TL3260.C65 1978 ISBN-13: 978-90-277-1204-2 DOl: 10.1007/978-94-009-9907-7 629.47'42 78-23657 II. Title. III. Series. e-ISBN-13: 978-94-009-9907-7 Published by D. Reidel Publishing Company, P. O. Box 17, Dordrecht, Holland. Sold and distributed in the U.S.A., Canada and Mexico by D. Reidel Publishir,g Company, Inc. Lincoln Building, 160 Old Derby Street, Hingham, Mass. 02043, U.S.A. Preparation of this material was supported by the Attitude Determination and Control Section, Goddard Space Flight Center, National Aeronautics and Space Administration under Contract No. NAS 5-11999 and by the System Sciences Division, Computer Sciences Corporation. (Reprinted 1980, 1984, 1985, 1986, 1988, 1991, 1994, 1995, 2000, 2002) All Rights Reserved Copyright © 1978 by D. Reidel Publishing Company, Dordrecht, Holland No part of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical including photocopying, recording or by any informational storage and retrieval system, without written permission from the copyright owner

LIST OF CONTRIBUTING AUTHORS All the authors are members of the technical staff in the Attitude Systems Operation, System Sciences Division, Computer Sciences Corporation. Sections written by each author are in brackets. John Aiello-B.S. (Astronomy), Villanova University [5.2, Appendix G] Jawaid Bashir-Ph.D. (Aerospace Engineering), M.S. (Electrical Engineering), Uni versity of Colorado; B.S. (Electrical Engineering), Karachi University, Pak istan [I8.I] Robert M. Beard-M.S. (Mathematics), B.S. (Physics), Auburn University [16.3] Bruce T. Blaylock-M.S. (Chemistry), University of Virginia; 8.S. (Chemistry), Eastern Montana College [6.3] Lily C. Chen-'-Ph.D. (Physics), University of Wisconsin, Madison; M.S. (Physics), University of Cincinnati; B.S. (Physics), National Taiwan University [7.1, 11.3, 11.4, 11.5, Chapter 10] Roger M. Davis-M.S. (Mechanical Engineering), Northeastern University; B.S. (Mechanical Engineering), University of Connecticut [16.4] Demosthenes Dialetis-Ph.D. (Physics), University of Rochester; B.Sc. (Physics), University of Athens, Greece [16.4] Lawrence Fallon, III-Ph.D., M.S. (Materials Science), University of Virginia; B.S. (Engineering Physics), Loyola College [6.4, 6.5, 7.6, 7.8, 13.4, 13.5, 21.3, Appendix D] B. L. Gambhir-Ph.D. (Physics), University of Maryland; M.Sc. (Physics), B.Sc. (Physics, Mathematics, English), Punjab University, India [6 . .1, 19.1] David M. Gottlieb-Ph.D. (Astronomy), University of Maryland; B.A. (Mathema tics), Johns Hopkins University [5.3, 5.6, 7.7] Mihaly G. Grell-M.S. (Physics), University of Sciences, Budapest [19.2] Dale Headrick-Ph.D., M.S. (Physics), Yale University; B.S. (Physics) Louisiana State University [6.6, 18.2, 19.4] Steven G. Hotovy-Ph.D. (Mathematics), University of Colorado; B.S. (Mathema tics), University of Notre Dame [7.2, 13.2, 13.3] James S. Legg, Jr.-M.S. (Physics), University of North Carolina; A.B. (Physics, Mathematics), Washington and Lee University [8.1,8.3,8.4,9.1] Gerald M. Lemer-Ph.D. (Physics), University of Maryland; B.A. (Physics), Johns Hopkins University [6.1, 6.2, 6.9, 7.1, 7.5, 9.2, 9.3, 12.2, 12.3, 18.1, 18.3, 19.5, Appendix F] Menachem Levitas-Ph.D. (Physics), University of Virginia; B.S. (Physics), Uni versity of Portland [7.3, 17.3] K. Liu-B.S. (Physics), National Taiwan University [4.3]

vi LIST OF CONTRIBUTING AUTHORS F. L. Markley-Ph.D. (Physics), University of California, Berkeley; B.E.P. (Engi neering Physics), Cornell University [7.4, 7.9: 12.1, 15.2, 16.1, 16.2, 17.1, Appendix C] Prafulla K. Misra-Ph.D., M.S. (Electrical Engineering), University of Maryland; B.Tech. (Electrical Engineering), Indian Institute of Technology, India [6.9] Janet Niblack-M.A. (Mathematics), University of Texas; B.A. (Mathematics), Florida State University [S.2] Michael Plett-Ph.D. (Physics), University of Virginia; B.S. (Physics), University of Cincinnati [5.1, 16.3, Appendix H] Paul V. Rigterink-Ph.D. (Astronomy), University of Pennsylvania; B.A. (Mathematics), Carleton College [13.4] John N. Rowe-Ph.D., M.S. (Electrical Engineering), Pennsylvania State Univer sity; M.A. (Physics), Western Michigan University; B.A. (Physics), Oakland University, Michigan [4.4, 5.4, 5.5] Ashok K. Saxena-M.S. (Aerospace Engineering), Virginia Polytechnic Institute and State University; B.E. (Mechanical Engineering), Jadavpur Univer sity, India [1S.4, Appendix I] Myron A. Shear-M.S. (Physics), University of Illinois; B.A. (Physics, Chemistry), Harvard University [20.1, 20.3, 21.1] Malcolm D. Shuster-Ph.D. (Physics), University of Maryland; S.B. (Physics), Massachusetts Institute of Technology [19.2] Peter M. Smith-Ph.D. (Chemistry), Georgetown University; M.Sc. (Spectroscopy), B.Sc. (Chemistry), Manchester University, England [11.1, 11.2, 21.4] Des R. Sood-D. Eng. Sc. (Mechanical Engineering), Columbia University; M.S. (Mechanical Engineering), Roorkee University, India; B.S. (Mechanical En gineering), Delhi University, India [6.7, 19.1] C. B. Spence, Jr.-Ph.D., M.S. (Physics), College of William and Mary; B.S. (Physics), University of Richmond [17.1, 17.2] Conrad R. Sturch-Ph.D. (Astronomy), University of California, Berkeley; M.S., B.A. (Physics), Miami University, Ohio [Appendix J] Gyanendra K. Tandon-Ph.D. (Physics), Yale University; M.Sc. (Electronics), B.Sc. (Physics, Mathematics), Allahabad University, India [17.4, 21.2, Appendix E] Vincent H. Tate-M.S., B.S. (Aerospace Engineering), Pennsylvania State Univer sity [15.3] James R. Wertz-Ph.D. (Physics), University of Texas, Austin; S.B. (Physics), Massachusetts InstituteofTechnology[4.1,4.2,9.4, 11.3, 11.4, 11.5, 13.1, 15.1; Chapters 1,2, 3, 10, 14, 22; Appendices A, B, K, L, M] Robert S. Williams-Ph.D. (Physics), University of Maryland; B.S. (Physics), California Institute of Technology [6.S, 7.10, 19.3] Kay yong-Ph.D., M.S. (Mechanical Engineering), Rensselaer Polytechnic Insti tute; B.S. (Mechanical Engineering), National Cheng-Kung University, Tai wan. [5.2]

FOREWORD Roger D. Werking Head, Attitude Determination and Control Section National Aeronautics and Space Administration/ Goddard Space Flight Center Extensiye work has been done for many years in the areas of attitude determination, attitude prediction, and attitude control. During this time, it has been difficult to obtain reference material that provided a comprehensive overview of attitude support activities. This lack of reference material has made it difficult for those not intimately involved in attitude functions to become acquainted with the ideas and activities which are essential to understanding the various aspects of spacecraft attitude support. As a result, I felt the need for a document which could be used by a variety of persons to obtain an understanding of the work which has been done in support of spacecraft attitude objectives. It is believed that this book, prepared by the Computer Sciences Corporation under the able direction of Dr. James Wertz, provides this type of reference. This book can serve as a reference for individuals involved in mission planning, attitude determination, and attitude dynamics; an introductory textbook for stu dents and professionals starting in this field; an information source for experimen ters or others involved in spacecraft-related work who need information on spacecraft orientation and how it is determined, but who have neither the time nor the resources to pursue the varied literature on this subject; and a tool for encouraging those who could expand this discipline to do so, because much remains to be done to satisfy future needs. The primary purpose of this book is to provide short descriptions of various aspects of attitude determination, prediction, and control with emphasis on the ground support which presently must be provided. The initial chapters provide the necessary background and describe environment models and spacecraft attitude hardware. The authors then present the fundamentals that are essential to a basic understanding of the activities in this area as well as flight-proven concepts which can be used as a basis for operational state-of-the-art activities or as a stepping stone to improved processes. In a limited fashion, Chapter 22 presents future activities which affect or are a part of spacecraft attitude support. It is not the intention of this book to advance the state of the art but rather to call attention to the work that has been done in the successful support of spacecraft attitude requirements and to stimulate future thinking.

PREFACE The purpose of this book is to summarize the ideas, data, and analytic techniques needed for spacecraft attitude determination and control in a form that is readable to someone with little or no previous background in this specific area. It has been prepared for those who have a physics or engineering background and therefore are familiar with the elementary aspects of Newtonian mechanics, vector algebra, and calculus. Summaries of pertinent facts in other are~s are presented without proof. This material has been prepared by 35 members of the technical staff of the Attitude Systems Operation of the System Sciences Division of Computer Sciences Corporation (CSC) for the Attitude Determination and Control Section of NASA's Goddard Space Flight Center. It necessarily reflects our experience in this area and therefore is concerned primarily with unmanned, Earth-orbiting spacecraft. None theless, the basic principles are sufficiently broad to be applicable to nearly any spacecraft. Chapters l, 2, 3, 10, and 15 provide introductory material at a more qualitative level than that of the other chapters. The suggested order of reading depends on the background and interest of the reader: I. Those who are primarily concerned with mission planning and analysis and who would like a general overview should read Chapters I, 2, 3, 10, 15, and 22. 2. Those who are primarly interested in attitude determination should read Chapters I and 2, Sections 3.1 through 3.3, Chapter 10, Appendices A and B, and Chapters II through 14. 3. Those who are primarily interested in attitude dynamics and control should read Chapters I and 2, Sections 3.1 through 3.3 and 12.1, Chapters 15 through 19, and Appendices C through H. 4. Those who are primarily interested in the space environment, attitude hardware, and data acquisition should read Chapters I through 9 and Appendices G through J. 5. Those who are primarily interested in the development of mission related software should read Chapters I and 2, Sections 3.1 through 3.3, Chapters 20 and 21, Chapters 8 and 9, Sections Il.l and 11.2, and Chapters 12, 4, 5, and 7. The International System of Units is used throughout the book and a detailed list of conversion factors is given in Appendix K. Because nearly all numerical work is now done with computers or hand calculators, all constants are given to essentially their full available accuracy. Acronyms have generally been avoided, except for spacecraft names. The full spacecraft names are listed in Appendix I, which also provides a cross-referenced list of the attitude hardware used on various spacecraft, including all those used as examples throughout the text. _ Because much of the material presented here has not appeared in the open literature, maJlY of the references are to corporate or government documents of limited Circulation.- To -improve the exchange of information, Computer Sciences

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