Selected Papers of Demetrios G. Magiros: Applied Mathematics, Nonlinear Mechanics, and Dynamical Systems Analysis

529 Pages·1985·19.157 MB·English

by  Demetrios G. Magiros (auth.), S. G. Tzafestas (eds.)

SELECTED PAPERS OF DEMETRIOS G. MAGIROS
DEMETRIOS G. MAGIROS
Selected Papers
of
Demetrios G. Magiros
Applied Mathematics, Nonlinear Mechanics,
and Dynamical Systems Analysis
Edited by
s.
G. Tzafestas
Electrical Engineering Department,
National Technical University. Athens. Greece
D. REIDEL PUBLISHING COMPANY
ACADEMIC PUBLISHERS GROUP
Published on behalf of the Greek Mathematical Society
library of Congress Cataloging in Publication Data
Magiros, Demetrios G.
Selected papers of Demetrios G. Magiros.
"Published on behalf of the Greek Mathematical Society."
Bibliography: p.
1. Mathematics-Collected works. 2. Nonlinear mechanics
Collected works. 3. System analysis-Collected works. I. Tzafestas, S. G.,
1939- II. Hellenike Mathematike Hetaireia (Greece)
QA3.M277 1985 510 85-2204
ISBN-13: 978-94-0 I 0-8869-5 eISBN-13: 978-94-009-5368-0
DOl: 10.1007/978-94-009-5368-0
Published by D. Reidel Publishing Company,
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Softcover reprint of the hardcover 1s t edition 1985
FOREWORD
The theory of nonlinear oscillations and stability of motion is a fundamental
part of the study of numerous real world phenomena. These phenomena,
particularly auto-oscillations of the first and second kind, capture, para
metric, subharmonic and ultraharmonic resonance, asymptotic behavior and
orbits' stability, constitute the core of problems treated in "Nonlinear
Mechanics", and their study is connected with the names of H. Poincare,
A. M. Lyapunov, N. M. Krylov and N. N. Bogolyubov.
Professor Demetrios Magiros, a widely known scientist in the theories of
oscillations and nonlinear differential equations, has devoted his numerous
works to this significant part of modern physical science. His scientific
results can be classified in the following way:
I) creation of methods of analysis of subharmonic resonances under the
nonlinear effect,
2) determination and analysis of the main modes of nonlinear oscillations
on the basis of infinite determinants,
3) analysis of problems of celestial mechanics,
4) classification of stability of solutions of dynamic systems concepts,
5) mathematical analogs of physical and social systems.
He has developed new methods and solutions for a great number
of difficult problems of nonlinear mechanics making a significant contri
bution to the theory and applications of the field.
Urgency, depth of perception of the considered phenomena, and practi
cal directness are characteristics of his work.
D. G. Magiros' scientific findings have been utilized in the research of
many scientists and can be applied to a variety of branches of mechanics,
physics and engineering, in which nonlinear oscillating processes and
problems of stability are involved.
Dr Magiros participated in several International Conferences, among
which the International Conferences on Nonlinear Oscillations held in Kiev
(1969, 1981).
v
vi FOREWORD
We are sure that the publication of Professor D. G. Magiros' Selected
Papers will be accepted by numerous specialists, working on the theory and
application of nonlinear oscillations, with great interest.
Yu. A. Mitropolsky, Academician
A.A. Martynyuk
Ukrainian Academy of Sciences
Kiev, USSR
IN MEMORY OF DIMITRIS MAGIROS
The Greek Mathematical Society is pleased to sponsor the publication
of the "Selected Papers" of a prominent member Dimitris G. Magiros,
honoring his memory and his work.
The distinguished mathematician graduated from the National Capo
distrian University of Athens and continued his studies and work in
the USA, where he dedicated his time principally to research in applied
mathematics and mechanics.
Our colleague Dimitris, in spite of the fact that he had spent most
of his scientific /(fe abroad, was an untiring collaborator of our Society
and has particularly shared our efforts for the advancement of mathematics
in Greece.
We believe that this volume, where most of his publications -scattered
in various scientific sources- are made collectively accessible, will facilitate
the propagation of the thoughts of an inspiring researcher for the benefit
of the international mathematical and systems science community.
The Governing Board of the
Greek Mathematical Society
vii
PREFACE
It is a distinct honor and privilege to be the editor of the Selected Papers of
Dr Demetrios G. Magiros.
Magiros' scientific work continued for about forty years bearing impor
tant contributions of theoretical and practical significance. His enormous
interest in the applications of mathematics, and the versatility of problems
which he has solved in the fields of his applications are reflected in these
papers.
Magiros' thoughts have left an impact on a variety of fields such as
nonlinear differential equations, subharmonic oscillations, principal modes
of nonlinear systems, celestial and orbital mechanics, stability analysis of
nonlinear dynamical systems, precessional phenomena, and other.
In his investigation, Magiros starts from a philosophical basis and
follows an axiomatic principle aiming always at the mathematical descri
ption and interpretation of the reality with emphasis on the applications.
Dr Magiros was an enthusiastic teacher with the talent to transmit both
the depth and width of his knowledge. I personally remember his excellent
lectures at NRC "Demokritos" in Athens (1973) on mathematical modeling
and stability of dynamical systems. His impressive set of lecture notes, listed
at the end of this book, covers a variety of topics from special functions and
transforms to numerical methods for solution of nonlinear differential
equations and optimal control problems.
We have decided with Mrs Helen Magiros to publish this volume hoping
that it would serve both as an important reference in the field of nonlinear
mechanics and dynamical systems, and as a source of inspiration to all
young mathematicians and systems scientists who are challenged to solve
real problems of our space age.
Many thanks are expressed to the Greek Mathematical Society for
encouraging and supporting this publication.
Spyros G. Tzafestas
ix
ACKNOWLEDGEMENTS
The publishers, the Greek Mathematical Society, the Editor, and Mrs Helen
Magiros wish to thank the following publishers for granting permission to
reprint the papers which appear in this volume (the identification of papers
refers to the List of Contents):
Athens Academy of Sciences (Practika-Proceedings of Athens Academy of
Sciences) for papers 2, 3, 4, 5, 8, 9, 10, 12, 13, 14, 15, 17, 21, 22, 23, 24, 29,
33, 34, 39 and 40.
Ukrainian Academy of Sciences (Ukrainian Mathematical Journal and
Matematicheskaya Fizika) for papers 41, 42 and 43.
John Wiley and Sons, Inc. (Communications of Pure and Applied Mathe
matics) for paper 7.
Academic Press, Inc. (Information and Control) for papers 16 and 31.
The American Institute of Physics (Journal of Mathematical Physics) for
paper 20.
The Franklin Institute (Journal of the Franklin Institute) for papers 25, 26,
27 and 32.
It is also acknowledged that papers 1, 18, 19 and 30 are reprinted from
Proceedings of the National Academy of Sciences (U.S.A.), papers 28, 37
and 38 from the Proceedings of International Astronautical Congresses held
in Madrid (1966), Buenos Aires (1969) and Brussels (1971), respectively, and
paper 36 from the Proceedings of the VIIIth Symposium on Space
Technology and Science (Tokyo, 1969).
The work described in the papers of the volume was done by D. G.
Magiros while he was with General Electric Co. (ReEntry Systems Opera
tion, Space Systems Division, Philadelphia, PA., U. S.A.).
Finally, the publishers, The Greek Mathematical Society, the Editor and
Mrs Magiros would like to thank A.J. Dennison, Joseph B. Keller and
George Reehl, co-authors of D. G. Magiros, for granting permission to
reprint the respective papers (7, 28, 29, 32, 37).
x
CONTENTS
PART I
APPLIED MA THEMA TICS AND MODELLING
1. A class of nonautonomous differential equations reducible to au
tonomous ones by an exact method. Proc. Natl. Acad. Sci., V.
58, no. 2 (1967): 412-419 [31]* ........................... 3
2. Nonlinear differential equations with several general solutions.
Proc. Acad. of Athens, V. 52 (1977): 221-229 [50]. Also: Ukr.
Math. J., V. 30, no. 2 (1978): 238-241 (see p. 499)....... II
3. The general solutions of nonlinear differential equations as fun
ctions of their arbitary constants. Proc. Acad. of Athens, V. 52
(1977): 524-532 [51]....................................... 20
4. Actual mathematical solutions of problems posed by reality, (I):
a classical procedure. Proc. Acad. of Athens, V. 45 (1970):
179-187 [39]..... .................. ..................... 29
5. Actual mathematical solutions of problems posed by reality, (II):
applications. Proc. Acad. of Athens, V. 46 (1971): 21-31 [40] 38
6. Physical problems discussed mathematically. Bull. Soc. Math.
Grece, nouv. ser., t. 611, fasc. I. (1965): 143-156 [25] ..... 49
7. Diffraction by a semi-infinite screen with a rounded end (with
Joseph B. Keller). Comm. Pure Appl. Math., V. 14, no. 3 (1961):
457-471 [16].............................................. 63
8. On the linearization of nonlinear models of the phenomena, pt. I:
linearization by exact methods. Proc. Acad. of Athens, V. 51
(1976): 659-668 [47]....................................... 78
9. On the linearization of nonlinear models of the phenomena, pt.
II: linearization by approximate methods. Proc. Acad. of Athens
V. 51 (1976): 669-683 [48]................................ 88
* Numbers in brackets refer to the Complete Chronological List of Magiros' publications.