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The second edition of Space Vehicle Dynamics and Controls includes over 260 pages of new material on the recent advances in dynamical modeling and control of advanced spacecraft such as agile imaging satellites equipped with control moment gyros, solar sails, and space solar power satellites. All of the new material contained in the second edition is based on my own or coauthored technical papers published in the Journal of Guidance, Control, and Dynamics and/or presented at various technical meetings during the past 10 years. Minor typographical errors of the first edition have been corrected. All of the material of the first edition, except the bibliography, has been retained.
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Space Vehicle Dynamics and Control
Second Edition
Bong Wie
Iowa State University
Ames, Iowa
EDUCATION SERIES
Joseph A. Schetz
Series Editor-in-Chief
Virginia Polytechnic Institute and State University
Blacksburg, Virginia
Published by
American Institute of Aeronautics and Astronautics, Inc.
1801 Alexander Bell Drive, Reston, VA 20191
“FM” — 2008/8/4 — 15:55 — iv — #4
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Cover photo credit: David Murphy, ATK Systems, Goleta, California; Olivier Boisard/
U3P/2006-www.U3P.net.
MATLAB
TM
is a registered trademark of The MathWorks, Inc.
American Institute of Aeronautics and Astronautics, Inc., Reston, Virginia
2345
Library of Congress Cataloging-in-Publication Data
Wie, Bong, 1952- -
Space vehicle dynamics and control / Bong Wie. - - 2nd ed.
p. cm.
Includes bibliographical references and index.
ISBN 978-1-56347-953-3 (alk. paper)
1. Space vehicles- -Dynamics. 2. Space vehicles- -Control systems. I. Title.
TL1050.W52 2008
629.47
1- -dc22
2008028777
Copyright © 2008 by the American Institute of Aeronautics and Astronautics, Inc. All rights
reserved. Printed in the United States of America. No part of this publication may be repro-
duced, distributed, or transmitted, in any form or by any means, or stored in a database or
retrieval system, without the prior written permission of the publisher.
Data and information appearing in this book are for informational purposes only. AIAA is
not responsible for any injury or damage resulting from use or reliance, nor does AIAA
warrant that use or reliance will be free from privately owned rights.
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Preface to the Second Edition
The second edition of Space Vehicle Dynamics and Controls includes over 260
pages of new material on the recent advances in dynamical modeling and control
of advanced spacecraft such as agile imaging satellites equipped with control
moment gyros, solar sails, and space solar power satellites. All of the new material
contained in the second edition is based on my own or coauthored technical papers
published in the Journal of Guidance, Control, and Dynamics and/or presented at
various technical meetings during the past 10 years. Minor typographical errors of
the first edition have been corrected. All of the material of the first edition, except
the bibliography, has been retained.
The first edition of this book consisted of four parts. The new Part 5 in the second
edition consists of the following four chapters:
Chapter 11 Control Moment Gyros for Agile Imaging Satellites
Chapter 12 Solar-Sail Dynamics and Control
Chapter 13 Solar-Sail Missions for Asteroid Deflection
Chapter 14 Attitude and Orbit Control of Space Solar Power Satellites
Part 5 is a collection of advanced spacecraft control problems and their prac-
tical solutions obtained by applying the fundamental principles and techniques
emphasized throughout the book.
Chapter 11 presents a comprehensive treatment of the geometric singularity
problem inherent to control-moment-gyro (CMG) systems, and it also describes
practical CMG steering algorithms and feedback control logic for large-angle,
rapid multitarget acquisition and pointing control of agile imaging satellites.
Chapter 12 is concerned with various dynamical modeling and control problems
of solar-sail spacecraft, and it also presents the analysis and design of solar-sail
attitude control systems for interplanetary solar-sailing missions as well as a solar-
sail flight validation mission in a sun-synchronous orbit.
Chapter 13 presents solar-sail mission applications to a complex astrodynamical
problem of changing the trajectory of near-Earth objects (NEOs) to mitigate their
impact threat to the Earth. This chapter is intended to provide the reader with an
overview of such a technically challenging, emerging astrodynamical problem of
deflecting NEOs using the nonnuclear alternatives such as the kinetic impactor,
gravity tractor, and solar sail.
Chapter 14 presents a preliminary conceptual design of an attitude and orbit
control system (AOCS) architecture for a very large, space solar power (SSP)
satellite in geostationary orbit.
xiii
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The solar-sail control research work described in Chapters 12 and 13 was
funded by the In-Space Propulsion Technology Program, which was managed
by NASA’s Science Mission Directorate in Washington, D.C., and implemented
by the In-Space Propulsion Technology Office at Marshall Space Flight Center in
Huntsville, Alabama. The program objective was to develop in-space propulsion
technologies that can enable or benefit near- and mid-term NASA space science
missions by significantly reducing cost, mass, or travel times. The research work
on the AOCS design for a large geostationary solar-power satellite described in
Chapter 14 was funded by the SSP Exploratory Research and Technology Program
of NASA.
I would like to thank the following colleagues for their direct and/or indi-
rect contributions to the new material of the second edition: Christopher Heiberg
and David Bailey, formerly at Honeywell Space Systems; David Murphy at ATK
Space Systems; Vaios Lappas at Surrey Space Centre, University of Surrey;
Bernd Dachwald, formerly at German Aerospace Center (DLR); Colin McInnes
at University of Strathclyde; Carlos Roithmayr at NASA Langley Research Cen-
ter; Edward Montgomery, Gregory Garbe, Joan Presson, Andy Heaton, Mark
Whorton, and Connie Carrington at NASA Marshall Space Flight Center; and
Christopher Moore at NASA Headquarters.
Finally, I wish to thank Tom Shih, Chairperson of the Aerospace Engineer-
ing Department at Iowa State University, for providing me with a challenging
opportunity to apply space vehicle dynamics and control technology to a complex
astrodynamical problem of changing the orbital trajectory of near-Earth objects to
mitigate their impact threat to Earth.
Bong Wie
June 2008
“FM” — 2008/8/4 — 15:55 — #9
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Table of Contents
Preface to the Second Edition ...............................xiii
Preface to the First Edition ................................. xv
Part 1. Dynamic Systems Modeling, Analysis, and Control
Chapter 1. Dynamic Systems Modeling and Analysis .............. 3
1.1 Matrix and Vector Analysis ............................. 3
1.2 Classical Mechanics ................................. 21
1.3 Dynamic Systems Analysis ............................ 71
Chapter 2. Dynamic Systems Control ....................... 121
2.1 Feedback Control Systems ........................... 121
2.2 Classical Frequency-Domain Methods ................... 123
2.3 Classical Gain-Phase Stabilization ...................... 136
2.4 Digital Control ................................... 152
2.5 Modern State-Space Methods ......................... 161
2.6 Stability Robustness Analysis ......................... 185
2.7 Robust Control of Uncertain Dynamic Systems ............. 205
Part 2. Orbital Dynamics and Control
Chapter 3. Orbital Dynamics ............................. 221
3.1 Two-Body Problem ................................ 221
3.2 Geometry of Conic Sections .......................... 229
3.3 Vis-Viva Equation ................................. 233
3.4 Kepler’s Time Equation .............................. 235
3.5 Orbital Position and Velocity .......................... 239
3.6 Orbital Perturbations ............................... 246
3.7 Circular Restricted Three-Body Problem .................. 255
3.8 Elliptic Restricted Three-Body Problem .................. 271
Chapter 4. Orbital Maneuvers and Control ................... 277
4.1 Launch Vehicle Trajectories ........................... 277
4.2 Orbit Injection .................................... 284
4.3 Single-Impulse Maneuvers ........................... 286
4.4 Hohmann Transfer ................................. 288
4.5 Interplanetary Flight ................................ 290
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