Applied Mathematics in Aerospace Science and Engineering

Transcription

1 Applied Mathematics in Aerospace Science and Engineering

2 MATHEMATICAL CONCEPTS AND METHODS IN SCIENCE AND ENGINEERING Series Editor: Angelo Miele George R. Brown School 0/ Engineering Rice University Recent volumes in this series: 31 NUMERICAL DERIVATIVES AND NONLINEAR ANALYSIS Harriet Kagiwada. Robert Kalaba. Nima Rasakhoo. and Karl Spingam 32 PRINCIPLES OF ENGINEERING MECHANICS Volume 1: Kinematics - The Geometry ofmotion. Millard F. Beatty. Jr. 33 PRINCIPLES OF ENGINEERING MECHANICS Volume 2: Dynamics - The Analysis of Motion. Millard F. Beatty. Jr. 34 STRUCTURAL OPTIMIZATION Volume 1: OptimaHty Criteria Edited by M. Save and W. Prager 3S OPTIMAL CONTROL APPLICA TIONS IN ELECTRIC POWER SYSTEMS G. S. Christensen. M. E. El-Hawary. and S. A. Soliman 36 GENERALIZED CONCAVITY Mordecai Avriel. Walter E. Diewert. Siegfried Schaible. and Israel Zang 37 MULTICRITERIA OPTIMIZATION IN ENGINEERING AND IN THE SCIENCES Edited by Wolfram Stadler 38 OPTIMAL LONG-TERM OPERATION OF ELECTRIC POWER SYSTEMS G. S. Christensen and S. A. Soliman 39 INTRODUCTION TO CONTINUUM MECHANICS FOR ENGINEERS Ray M. Bowen 40 STRUCTURAL OPTIMIZATION Volume 2: Mathematical Programming. Edited by M. Save and W. Prager 41 OPTIMAL CONTROL OF DISTRIBUTED NUCLEAR REACTORS G. S. Christensen, S. A. Soliman. and R. Nieva 42 NUMERICAL SOLUTION OF INTEGRAL EQUATIONS Edited by Michael A. Golberg 43 APPLIED OPTIMAL CONTROL THEORY OF DISTRIBUTED SYSTEMS K. A. Lurie 44 APPLIED MATHEMATICS IN AEROSPACE SCIENCE AND ENGINEERING Edited by Angelo Miele and Attilio Salvetti A Continuation Order Plan is available for this series. A continuation order will bring delh'ery of each new volume immediately upon publication. Volumes are billed only upon actual shipment. For further information please contact the publisher.

3 Applied Mathetnatics in Aerospace Science and Engineering Edited by Angelo Miele Riee University Houston, Texas and Attilio Salvetti University of Pisa Pisa, Italy Springer Science+Business Media, LLC

4 Library of Congress Cataloging in Publication Data Applied mathematics in aerospace science and engineering / edited by Angelo Miele and Attilio Salvetti. p. cm.-(mathematical concepts and methods in science and engineering; 44) Proceedings of the meeting held in Erice, Sicily, Italy, Sept. 3-10, Includes bibliographical references and index. 1. Astronautics-Mathematics-Congresses. 2. Space flight-mathematical models Congresses. 3. Fluid mechanics-mathematics-congresses. 4. Airplanes-Design and construction-mathematics-congresses. I. Miele, Angelo. 11. Salvetti, A. III. Series. 1L780.A '015'I--dc20 CIP Proceedings of a meeting on Applied Mathematics in the Aerospace Field, held September 3-10, 1991, in Erice, Italy ISBN ISBN (ebook) DOI / Springer Science+Business Media New York Originally published by Plenum Press, New York in Softcover reprint of the hardcover 1 st edition 1994 All rights reserved No part of this book may be reproduced, stored in a retrieval system, or transmilted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording, or otherwise, without wrilten permission from the Publisher

5 Contributors E. Antona, Department of Aerospace Engineering, Polytechnic of Turin, Turin, Italy M. Borri, Department of Aerospace Engineering, Polytechnic of Milan, Milan, Italy A. J. Calise, School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, Georgia C. Carlenzoli, Department of Mathematics, Catholic University of the Sacred Heart, Brescia, Italy C. Cercignani, Department of Mathematics, Polytechnic of Milan, Milan, Italy A. Frediani, Department of Aerospace Engineering, University of Pisa, Pisa, Italy C. Jänsch, Institute for Robotics and System Dynamies, DFVLR, Oberpfaffenhofen, Germany; present address: Institute of Mechanics and Control of Flight, University of Stuttgart, Stuttgart, Germany B. S. Lee, Aero-Astronautics Group, Rice University, Houston, Texas G. Leitmann, College of Engineering, University of California, Berkeley, California v

6 vi Contributors R. W. MacCormack, Department of Aeronautics and Astronautics, Stanford University, Stanford, California C. Maccone, Space Systems Group, Alenia Spazio, Turin, Italy A. Miele, Aero-Astronautics Group, Rice University, Houston, Texas L. Morino, Department of Mechanics and Automatics, Third University of Rome, Rome, Italy H. J. Pesch, Department of Mathematics, Technical University, POß , Munich, Germany A. Quarteroni, Department of Mathematics, Polytechnic of Milan, Milan, Italy G. Sachs, Department of Flight Mechanics and Control, Technical University, Munich, Germany A. Salvetti, Department of Aerospace Engineering, University of Pisa, Pisa, Italy P. Santini, Department of Aerospace Engineering, University of Rome-l, Rome, Italy K. Schnepper, Institute for Robotics and System Dynamics, DFVLR, Oberpfaffenhofen, Germany J. Sobieszczanski-Sobieski, Structural Dynamics Division, NASA Langley Research Center, Hampton, Virginia A. Valli, Department of Mathematics, University of Trento, Povo, Trento, Italy M. Van Dyke, Departments of Mechanical Engineering and (by courtesy) Aeronautics and Astronautics, Stanford University, Stanford, California K. H. Weil, Institute for Mechanics and Control of Flight, University of Stuttgart, Stuttgart, Germany

7 Preface This book contains the proceedings ofthe meeting on "Applied Mathematics in the Aerospace Field," held in Erice, Sicily, Italy from September 3 to September 10, The occasion of the meeting was the 12th Course of the School of Mathematics "Guido Stampacchia," directed by Professor Franco Giannessi of the University of Pisa. The school is affiliated with the International Center for Scientific Culture "Ettore Majorana," which is directed by Professor Antonino Zichichi of the University of Bologna. The objective of the course was to give a perspective on the state-ofthe-art and research trends concerning the application of mathematics to aerospace science and engineering. The course was structured with invited lectures and seminars concerning fundamental aspects of differential equations, mathematical programming, optimal control, numerical methods, perturbation methods, and variational methods occurring in flight mechanics, astrodynamics, guidance, control, aircraft design, fluid mechanics, rarefied gas dynamics, and solid mechanics. The book includes 20 chapters by 23 contributors from the United States, Germany, and Italy and is intended to be an important reference work on the application of mathematics to the aerospace field. It reflects the belief of the course directors that strong interaction between mathematics and engineering is beneficial, indeed essential, to progresses in both areas. The book is organized into four parts. Part 1 deals with analytical and numerical methods in fluid mechanics and includes six chapters by M. Van Dyke, R. W. MacCormack, C. Cercignani, L. Morino, C. Carlenzoli, A. Quarteroni, and A. VaIli. Part 2 refers to analytical and numerical methods in fluid mechanics and includes five chapters by A. J. Calise, H. J. Pesch, G. Sachs, C. Jänsch, K. Schnepper, K. H. WeIl, A. Miele, and B. S. Lee. Part 3 contains analytical and numerical methods in dynamics and structures and includes five chapters by G. Leitmann, P. Santini, M. Borri, A. Frediani, and E. Antona. Part 4 deals with mathematical techniques and includes four chapters by J. Sobieszczanski-Sobieski, P. Santini, and C. Maccone. vii

8 viii Preface In addition to expressing their thanks to Professors Giannessi and Zichichi, the course directors acknowledge the organizational and technical contributions of Professor Aldo Frediani of the University of Pisa. Angelo Miele Houslon, Texas Attilio Salvetti Pisa, Ilaly

9 Contents Part 1: Fluid Mechanies 1. Slow Variations in Fluid Mechanics 3 M. Van Dyke 2. Computer-Extended Series in Fluid Mechanics M. Van Dyke 3. Solving the Equations of Compressible Viscous Flow about Aerospace Configurations R. W. MacCormack 4. Mathematical Problems in the Gas Dynamics of High-Altitude Flight C. Cercignani 5. Toward a Unification of Potential and Viscous Aerodynamies: Boundary Integral Formulation L. Morino 6. Numerical Solution of the Navier-Stokes Equations for Viscous Compressible Flows C. Carlenzoli, A. Quarteroni, and A. Valli ix

10 x Contents Part 2: Flight Mechanics and Control 7. Singular Perturbations in F1ight Mechanies A. J. Calise 8. Multi-Phase Trajectory Optimization Methods with Applications to Hypersonie Vehicles C. Jänsch, K. Schnepper, and K. H. Weil 9. Offline and Online Computation of Optimal Trajectories in the Aerospace Field H. J. Pesch 10. Optimal Wind Energy Extraetion for Dynamic Soaring G. Sachs 11. Introduction to Optimal Trajectories for Aeroassisted Orbital Transfer A. Miele and B. S. Lee Part 3: Dynamics and Struetures 12. Lyapunov Stability Theory Based Control of Uncertain Dynamical Systems G. Leitmann 13. Stability Problems in Space Flight Mechanics P. Santini 14. Numerical Approximations in Analytical Dynamics M. Borri

11 Contents xi 15. Effects of Plasticity of Metallic Materials on Fatigue and Fracture Mechanics A. Frediani 16. Mathematical Models and Their Use in Engineering E. Antona 395 Part 4: Mathematical Techniques 17. Recent Mathematical Methods for Engineering System Design, Part 1: Overcoming Bellman's Curse of Dimensionality in Large Optimization Problems J. Sobieszczanski-Sobieski 18. Recent Mathematical Methods for Engineering System Design, Part 2: System Approach in Engineering Optimization J. Sobieszczanski-Sobieski 19. Numerical Treatment of Quasi-Singular Integrals in Dynamic Response Problems P. Santini 20. Symbolic Calculus Computations in the Aerospace Field C. Maccone 493 Index