Applied cartesian tensors for aerospace simulations PDF
Preview Applied cartesian tensors for aerospace simulations
Purchased from American Institute of Aeronautics and Astronautics Applied Cartesian Tensors for Aerospace Simulations David M. Henderson Lago Vista, Texas &AIAA 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 20191-4344 Purchased from American Institute of Aeronautics and Astronautics American Institute of Aeronautics and Astronautics, Inc., Reston, Virginia 1 2 3 45 Library of Congress Cataloging-in-Publication Data Henderson, David M. (David Melvin), 1935- Applied cartesian tensors for aerospace simulations/David M. Henderson. p. cm. — (AIAA education series) Includes bibliographical references and index. ISBN 1-56347-793-9 1. Flight simulators—Mathematics. 2. Calculus of tensors. I. Title. II. Series. TL712.5.H462006 629.132'52078—dc22 2006000085 Copyright © 2006 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 reproduced, 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 information 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. Purchased from American Institute of Aeronautics and Astronautics This page intentionally left blank Purchased from American Institute of Aeronautics and Astronautics AIAA Education Series Editor-in-Chief Joseph A. Schetz Virginia Polytechnic Institute and State University Editorial Board Takahira Aoki Rakesh K. Kapania University of Tokyo Virginia Polytechnic Institute and State University Edward W. Ashford Brian Landrum Karen D. Barker University of Alabama, Huntsville The Brake Corporation Tim C. Lieu wen Robert H. Bishop Georgia Institute of Technology University of Texas at Austin Achille Messac Claudio Brimo Rensselaer Polytechnic Institute University of Rome Michael Mohaghegh Aaron R. Byerley The Boeing Company U. S. Air Force Academy Conrad F. Newberry Richard Colgren Naval Postgraduate School University of Kansas Mark A. Price Kajal K. Gupta Queen's University Belfast NASA Dryden Flight Research Center James M. Rankin RikardB. Heslehurst Ohio University Australian Defence Force Academy David K. Schmidt David K. Holger University of Colorado, Iowa State University Colorado Springs David M. Van Wie Johns Hopkins University Purchased from American Institute of Aeronautics and Astronautics This page intentionally left blank Purchased from American Institute of Aeronautics and Astronautics This page intentionally left blank Purchased from American Institute of Aeronautics and Astronautics Foreword We are pleased to present Applied Cartesian Tensors for Aerospace Simulations by David M. Henderson. This compact volume covers the use of tensors in the analysis of navigation, guidance, and control of aerospace vehicles. There are four chapters and four appendices, and the book is more than 200 pages long. David Henderson is very well qualified to write on the subject, because of his long and broad experience in the field. The AIAA Education Book Series aims to cover a very broad range of topics in the general aerospace field, including basic theory, applications and design. Information about the complete list of titles can be found on the last pages of this volume. The philosophy of the series is to develop textbooks that can be used in a university setting, as instructional materials for continuing education and professional development courses, and also as books that can serve as the basis for independent study. Suggestions for new topics or authors are always welcome. Joseph A. Schetz Editor-in-Chief AIAA Education Book Series VII Purchased from American Institute of Aeronautics and Astronautics This page intentionally left blank Purchased from American Institute of Aeronautics and Astronautics Table of Contents Preface........................................................................... xi Acknowledgments.............................................................. xiii Chapter 1. Geometric Concepts in the Absence of Mass and Gravitation................................................... 1 1.1 Position Transformation............................................... 2 1.2 Properties of the Transformation Matrix ............................. 9 1.3 Euler Angles and the Transformation Matrix ........................ 18 1.4 Euler's Theorem and Four Parameter Methods ...................... 27 1.5 Differentiation of the Transformation Matrix ........................ 41 1.6 Transformation Equations for Velocity and Acceleration............ 52 Chapter 2. Motion of a Point Mass in Gravitational Space............. 59 2.1 Point Mass: Mathematical Descriptions.............................. 60 2.2 Point Mass and Gravitation ........................................... 66 2.3 Point Mass Motion Relative to Earth-Based Coordinates ........... 82 2.4 Point Mass Motion Relative to Space-Based Coordinates........... 94 Chapter 3. W-Body Gravitational Space and Rigid Body Motion ..... 107 3.1 TV-Body Mass Systems: Mathematical Descriptions................. 107 3.2 Rigid Body Dynamics................................................. 120 Chapter4. Flight Vehicle Motion .......................................... 129 4.1 Modeling Gravitational Environments for Aerospace Vehicles ..... 130 4.2 Forces and Moments on the Flight Vehicle........................... 139 4.3 Flight Vehicle Motion Simulations ................................... 171 4.4 Space Vehicle Motion Using Mean Orbital Elements ............... 176 Appendix A. Relationships for Three-Axis Euler Rotational Sequences ..................................... 187 Appendix B. C-W State Transition Matrix for LVLH Relative Motion ................................... 195 Appendix C. Integral Lists for Computer Simulation Algorithms..... 197 IX
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