Dynamical Systems and Control Volume 1 Theory of Integro-Differential Equations V. Lakshmikantham and M. Rama Mohana Rao Volume 2 Stability Analysis: Nonlinear Mechanics Equations A.A. Martynyuk Volume 3 Stability of Motion of Nonautonomous Systems (Method of Limiting Equations) J. Kato, A.A. Martynyuk, and A.A. Shestakov Volume 4 Control Theory and its Applications E.O. Roxin Volume 5 Advances in Nonlinear Dynamics Edited by S. Sivasundaram and A.A. Martynyuk Volume 6 Solving Differential Problems by Multistep Initial and Boundary Value Methods L. Brugnano and D. Trigiante Volume 7 Dynamics of Machines with Variable Mass L. Cveticanin Volumes 8 Optimization of Linear Control Systems: Analytical Methods and Computational Algorithms F.A. Aliev and VB. Larin Volume 9 Dynamics and Control Edited by G. Leitmann, F.E. Udwadia and A.V Kryazhimskii Volume 10 Volterra Equations and Applications Edited by C. Corduneanu and I.W. Sandberg Volume 11 Nonlinear Problems in Aviation and Aerospace Edited by S. Sivasundaram Volume 12 Stabilization of Programmed Motion E. Ya. Smirnov Volume 13 Advances in Stability Theory at the End of the 20th Century A.A. Martynyuk Volume 14 Dichotomies and Stability in Nonautonomous Linear Systems Yu A. Mitropolskii, A.M. Samoilenko, and V. L Kulik Volume 15 Almost Periodic Solutions of Differential Equations in Banach Spaces Y. Hino, T. Naito, Nguyen Van Minh, and Jong Son Shin Volume 16 Functional Equations with Causal Operators C. Corduneanu Volume 17 Optimal Control of Growth of Wealth of Nations E.N. Chukwu Volume 18 Stability and Stabilization of Nonlinear Systems with Random Structure I. Ya Kats and A.A Martynyuk Volume 19 Lyapunov Method & Certain Differential Games V.I. Zhukovskii Volume 20 Stability of Differential Equations with Aftereffect N.V. Azbelev and P.M. Simonov Volume 21 Asymptotic Methods in Resonance Analytical Dynamics E.A. Grebenikov, Yu. A. Mitropolsky and Yu. A. Ryabov Volume 22 Dynamical Systems and Control Edited by Firdaus E. Udwadia, H.I. Weber, and George Leitmann Stability and Control: Theory, Methods and Applications A series of books and monographs on the theory of stability and control Edited by A.A. Martynyuk Institute of Mechanics, Kiev, Ukraine and V. Lakshmikantham Florida Institute of Technology, USA Stability and Control: Theory, Methods and Applications Volume 22 E DITED BY Firdaus E. Udwadia University of Southern California USA H. I. Weber Pontifical Catholic University of Rio de Janeiro Brazil George Leitmann University of California, Berkeley USA CHAPMAN & HALL/CRC A CRC Press Company Boca Raton London New York Washington, D.C. Dynamical Systems and Control This book contains information obtained from authentic and highly regarded sources. Reprinted material is quoted with permission, and sources are indicated. A wide variety of references are listed. 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Udwadia, G. Leitmann, and H.I. Weber p. cm. (Stability and control ; v.22) Includes bibliographical references and index. ISBN 0-415-30997-2 (alk. paper) 1. Dynamics. 2. Differentiable dynamical systems. 3. Control theory. I. Udwadia, F.E. II. Leitmann, George. III. Weber, H. (Hans) IV. International Workshop on Dynamics and Control (11th : 2000 : Rio de Janeiro, Brazil) V. Title. VI. Series. QA845.D93 2004 003‘.85—dc22 2004043591 TF1677-discl.fm Page 1 Monday, April 12, 2004 2:34 PM “DynamicalSystems” — 2004/3/7 — page #v Contents List of contributors vii Preface xi Part I A geometric approach to the mechanics of densely folded media Luiz Bevilacqua 3 On a general principle of mechanics and its application to general non-ideal nonholonomic constraints Firdaus E. Udwadia 21 Mathematical analysis of vibrations of nonhomogeneous filament with one end load Marianna A. Shubov 33 Expanded point mapping analysis of periodic systems Henryk Flashner and Michael Golat 53 A preliminary analysis of the phase portrait’s structure of a nonlinear pendulum-mechanical system using the perturbed Hamiltonian formulation D´ebora Belato, Hans Ingo Weber and Jos´e Manoel Balthazar 77 A review of rigid-body collision models in the plane Edson Cataldo and Rubens Sampaio 91 Part II Optimal round-trip Earth–Mars trajectories for robotic flight and manned flight A. Miele, T. Wang and S. Mancuso 109 Aircraft take-off in windshear: a viability approach N. Seube, R. Moitie and G. Leitmann 127 Stability of torsional and vertical motion of suspension bridges subject to stochastic wind forces N.U. Ahmed 145 “DynamicalSystems” — 2004/3/7 — page #vi vi Contents Time delayed control of structural systems Firdaus E. Udwadia, Hubertus F. von Bremen, Ravi Kumar and Mohamed Hosseini 163 Robust real- and discrete-time control of a steer-by-wire system in cars Eduard Reithmeier 207 Optimal placement of piezoelectric sensor/actuators for smart structures vibration control Vicente Lopes, Jr., Valder Steffen, Jr. and Daniel J. Inman 221 A review of new vibration issues due to non-ideal energy sources J.M. Balthazar, R.M.L.R.F Brasil, H.I. Weber, A. Fenili, D. Belato, J.L.P. Felix and F.J. Garzelli 237 Identification of flexural stiffness parameters of beams Jos´e Jo˜ao de Esp´ındola and Jo˜ao Morais da Silva Neto 259 Active noise control caused by airflow through a rectangular duct Seyyed Said Dana, Naor Moraes Melo and Simplicio Arnaud da Silva 271 Dynamical features of an autonomous two-body floating system Helio Mitio Morishita and Jess´e Rebello de Souza Junior 283 Dynamics and control of a flexible rotating arm through the movement of a sliding mass Agenor de Toledo Fleury and Frederico Ricardo Ferreira de Oliveira 299 Measuring chaos in gravitational waves Humberto Piccoli and Fernando Kokubun 319 Part III Estimation of the attractor for an uncertain epidemic model E. Cr¨uck, N. Seube and G. Leitmann 337 Liar paradox viewed by the fuzzy logic theory Ye-Hwa Chen 351 Pareto-improving cheating in an economic policy game Christophe Deissenberg and Francisco Alvarez Gonzalez 363 Dynamic investment behavior taking into account ageing of the capital goods Gustav Feichtinger, Richard F. Hartl, Peter Kort and Vladimir Veliov 379 A mathematical approach towards the issue of synchronization in neocortical neural networks R. Stoop and D. Blank 393 Optimal control of human posture using algorithms based on consistent approximations theory Luciano Luporini Menegaldo, Agenor de Toledo Fleury and Hans Ingo Weber 407 Subject Index 431 “DynamicalSystems” — 2004/3/7 — page #vii Contributors N.U. Ahmed, School of Information Technology and Engineering, Department of Mathematics, University of Ottawa, Ottawa, Ontario Jos´e Manoel Balthazar, Instituto de Geociˆencias e Ciˆencias Exatas – UNESP – Rio Claro, Caixa Postal 178, CEP 13500-230, Rio Claro, SP, Brasil D´ebora Belato, DPM – Faculdade de Engenharia Mecˆanica – UNICAMP, Caixa Postal 6122, CEP 13083-970, Campinas, SP, Brasil Luiz Bevilacqua, Laborat´orio Nacional de Computa¸c˜ao Cient´ıfica – LNCC, Av. Get´ulio Vargas 333, Rio de Janeiro, RJ 25651-070, Brasil D. Blank, Institut f¨ur Neuroinformatik, ETHZ/UNIZH, Winterthurerstraße 190, CH-8057 Z¨urich R.M.L.R.F. Brasil, Dept. of Structural and Foundations Engineering, Polytech- nic School, University of S˜ao Paulo, P.O. Box 61548, 05424-930, SP, Brazil Edson Cataldo, Universidade Federal Fluminense (UFF), Departamento de Mate- m´atica Aplicada, PGMEC-Programa de P´os-Gradua¸c˜ao em Engenharia Mecˆanica, Rua M´ario Santos Braga, S/No-24020, Centro, Niter´oi, RJ, Brasil Ye-Hwa Chen, The George W. Woodruff School of Mechanical Engineering, Geor- gia Institute of Technology, Atlanta, Georgia 30332, USA E. Cr¨uck, Laboratoire de Recherches Balistiques et A´erodynamiques, BP 914, 27207 Vernon Cedex, France Seyyed Said Dana, Graduate Studies in Mechanical Engineering, Mechanical Engineering Department, Federal University of Paraiba, Campus I, 58059-900 Joao Pessoa, Paraiba, Brazil Christophe Deissenberg, CEFI, UMR CNRS 6126, Universit´e de la M´editerran´ee (Aix-Marseille II), Chˆateau La Farge, Route des Milles, 13290 Les Milles, France Jos´e Jo˜ao de Esp´ındola, Department of Mechanical Engineering, Federal Uni- versity of Santa Catarina, Brazil Gustav Feichtinger, Institute for Econometrics, OR and Systems Theory, Uni- versity of Technology, Argentinierstrasse 8, A-1040 Vienna, Austria J.L.P. Felix, School of Mechanical Engineering, UNICAMP, P.O. Box 6122, 13800- 970, Campinas, SP, Brazil A. Fenili, School of Mechanical Engineering, UNICAMP, P.O. Box 6122, 13800- 970, Campinas, SP, Brazil “DynamicalSystems” — 2004/3/7 — page #viii viii Contributors Henryk Flashner, Department of Aerospace and Mechanical Engineering, Uni- versity of Southern California, Los Angeles, CA 90089-1453 Agenor de Toledo Fleury, Control Systems Group/Mechanical & Electrical En- gineering Division, IPT/ S˜ao Paulo State Institute for Technological Research, P.O. Box 0141, 01064-970, S˜ao Paulo, SP, Brazil F.J. Garzelli, Dept. of Structural and Foundations Engineering, Polytechnic School, University of S˜ao Paulo, P.O. Box 61548, 05424-930, SP, Brazil Michael Golat, Department of Aerospace and Mechanical Engineering, University of Southern California, Los Angeles, CA 90089-1453 Francisco Alvarez Gonzalez, Dpto. Economia Cuantitativa, Universidad Com- plutense, Madrid, Spain Richard F. Hartl, Institute of Management, University of Vienna, Vienna, Austria Daniel J. Inman, Center for Intelligent Material Systems and Structures, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061-0261, USA Fernando Kokubun, Department of Physics, Federal University of Rio Grande, Rio Grande, RS, Brazil Peter Kort, Department of Econometrics and Operations Research and CentER, Tilburg University, Tilburg, The Netherlands G. Leitmann, College of Engineering, University of California, Berkeley CA 94720, USA Vicente Lopes, Jr., Department of Mechanical Engineering – UNESP-Ilha Solte- ira, 15385-000 Ilha Solteira, SP, Brazil S. Mancuso, Rice University, Houston, Texas, USA Naor Moraes Melo, Graduate Studies in Mechanical Engineering, Mechanical Engineering Department, Federal University of Paraiba, Campus I, 58059-900 Joao Pessoa, Paraiba, Brazil Luciano Luporini Menegaldo, S˜ao Paulo State Institute for Technological Re- search, Control System Group / Mechanical and Electrical Engineering Division, P.O. Box 0141, CEP 01604-970, S˜ao Paulo-SP, Brazil A. Miele, Rice University, Houston, Texas, USA Helio Mitio Morishita, University of S˜ao Paulo, Department of Naval Architec- ture and Ocean Engineering, Av. Prof. Mello Moraes, 2231, Cidade Universit´aria 05508-900, S˜ao Paulo, SP, Brazil Frederico Ricardo Ferreira de Oliveira, Mechanical Engineering Department/ Escola Polit´ecnica, USP – University of S˜ao Paulo, P.O. Box 61548, 05508-900, S˜ao Paulo, SP, Brazil Humberto Piccoli, Department of Materials Science, Federal University of Rio Grande, Rio Grande, RS, Brazil Eduard Reithmeier, Institut f¨ur Meß- und Regelungstechnik, Universit¨at Han- nover, 30167 Hannover, Germany Rubens Sampaio, Pontif´ıcia Universidade Cat´olica do Rio de Janeiro (PUC-Rio), Departamento de Engenharia Mecˆanica, Rua Marquˆes de S˜ao Vicente, 225, 22453- 900, G´avea, Rio de Janeiro, Brasil “DynamicalSystems” — 2004/3/7 — page #ix Contributors ix N. Seube, Ecole Nationale Sup´erieure des Ing´enieurs des Etudes et Techniques d’Armement, 29806 BREST Cedex, France Marianna A. Shubov, Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX, 79409, USA Jo˜ao Morais da Silva Neto, Department of Mechanical Engineering, Federal University of Santa Catarina, Brazil Simplicio Arnaud da Silva, Graduate Studies in Mechanical Engineering, Me- chanical Engineering Department, Federal University of Paraiba, Campus I, 58059- 900 Joao Pessoa, Paraiba, Brazil Jess´e Rebello de Souza Junior, University of S˜ao Paulo, Department of Naval Architecture and Ocean Engineering, Av. Prof. Mello Moraes, 2231, Cidade Uni- versit´aria 05508-900, S˜ao Paulo, SP, Brazil Valder Steffen, Jr., School of Mechanical Engineering Federal University of Uber- lˆandia, 38400-902 Uberlˆandia, MG, Brazil R. Stoop, Institut f¨ur Neuroinformatik, ETHZ/UNIZH, Winterthurerstraße 190, CH-8057 Z¨urich F.E. Udwadia, Department of Aerospace and Mechanical Engineering, Civil En- gineering, Mathematics, and Operations and Information Management, 430K Olin Hall, University of Southern California, Los Angeles, CA 90089-1453 Vladimir Veliov, Institute for Econometrics, OR and Systems Theory, University of Technology, Argentinierstrasse 8, A-1040 Vienna, Austria T. Wang, Rice University, Houston, Texas, USA Hans Ingo Weber, DEM - Pontif´ıcia Universidade Cat´olica – PUC – RJ, CEP 22453-900, Rio de Janeiro, RJ, Brasil . Udwadia “DynamicalSystems” — 2004/3/7 — page #xii “DynamicalSystems” — 2004/3/4 — page #1 PART I “DynamicalSystems” — 2004/3/4 — page #2 “DynamicalSystems”. Cataloging-in-Publication Data Dynamical systems and control / edited by F.E. Udwadia, G. Leitmann, and H.I. Weber p. cm. (Stability and control ; v.22) Includes