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Nonlinear Stability and Bifurcation Theory: An Introduction for Engineers and Applied Scientists - Softcover
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Book by Troger Hans Steindl Alois
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Every student in engineering or in other fields of the applied sciences who has passed through his curriculum knows that the treatment of nonlin ear problems has been either avoided completely or is confined to special courses where a great number of different ad-hoc methods are presented. The wide-spread believe that no straightforward solution procedures for nonlinear problems are available prevails even today in engineering cir cles. Though in some courses it is indicated that in principle nonlinear problems are solveable by numerical methods the treatment of nonlinear problems, more or less, is considered to be an art or an intellectual game. A good example for this statement was the search for Ljapunov functions for nonlinear stability problems in the seventies. However things have changed. At the beginning of the seventies, start ing with the work of V.1. Arnold, R. Thom and many others, new ideas which, however, have their origin in the work of H. Poincare and A. A. Andronov, in the treatment of nonlinear problems appeared. These ideas gave birth to the term Bifurcation Theory. Bifurcation theory allows to solve a great class of nonlinear problems under variation of parameters in a straightforward manner.
Reseña del editor
There has been a tremendous progress in the mathematical treatment of nonlinear dynamical systems over the past two decades. This book tries to make this progress in the field of stability theory available to scientists and engineers. A unified and systematic treatment of the different types of loss of stability of equilibrium positions of statical and dynamical systems and of periodic solutions of dynamical systems is given by means of the methods of bifurcation and singuality theory. The reader needs only a background in mathematics as it is usually taught to undergraduates in engineering and, having read this book, he should be able to treat nonlinear stability and bifurcation problems himself in a straightforward way. Among others, concepts such as center manifold theory, the method of Ljapunov-Schmidt, normal form theory, unfolding theory, bifurcation diagrams, classifications and bifurcations in symmetric systems are discussed, as far as they are relevant in applications. Most important for the whole representation is a set of examples taken from mechanics and engineering showing the usefulness of the above mentioned concepts. These examples include buckling problems of rods, plates and shells and furthermore the loss of stability of the motion of road and rail vehicles, of a simple robot, and of fluid conveying elastic tubes. With these examples, questions like symmetry breaking, pattern formation, imperfection sensitivity, transition to chaos and correct modelling of systems are touched. Finally a number of selected FORTRAN-routines should encourage the reader to treat his own problem.
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- VerlagSpringer
- Erscheinungsdatum1991
- ISBN 10 3211822925
- ISBN 13 9783211822920
- EinbandTapa blanda
- SpracheEnglisch
- Anzahl der Seiten424
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NONLINEAR STABILITY AND BIFURCATION THEORY : AN INTRODUCTION FOR ENGINEERS AND APPLIED SCIENTISTS
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Nonlinear Stability and Bifurcation Theory: An Introduction for Engineers and Applied Scientists
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Nonlinear Stability and Bifurcation Theory : An Introduction for Engineers and Applied Scientists
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Taschenbuch. Zustand: Neu. Druck auf Anfrage Neuware - Printed after ordering - Every student in engineering or in other fields of the applied sciences who has passed through his curriculum knows that the treatment of nonlin ear problems has been either avoided completely or is confined to special courses where a great number of different ad-hoc methods are presented. The wide-spread believe that no straightforward solution procedures for nonlinear problems are available prevails even today in engineering cir cles. Though in some courses it is indicated that in principle nonlinear problems are solveable by numerical methods the treatment of nonlinear problems, more or less, is considered to be an art or an intellectual game. A good example for this statement was the search for Ljapunov functions for nonlinear stability problems in the seventies. However things have changed. At the beginning of the seventies, start ing with the work of V.1. Arnold, R. Thom and many others, new ideas which, however, have their origin in the work of H. Poincare and A. A. Andronov, in the treatment of nonlinear problems appeared. These ideas gave birth to the term Bifurcation Theory. Bifurcation theory allows to solve a great class of nonlinear problems under variation of parameters in a straightforward manner. Artikel-Nr. 9783211822920
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Nonlinear Stability and Bifurcation Theory
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Springer Vienna, 1991
ISBN 10: 3211822925
ISBN 13: 9783211822920
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