Dynamics and Bifurcations of Non-Smooth Mechanical Systems

Dynamics and Bifurcations of Non-Smooth Mechanical Systems PDF Author: Remco Leine
Publisher: Springer Science & Business Media
ISBN: 9783540219873
Category : Mathematics
Languages : en
Pages : 252

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Book Description
This monograph combines the knowledge of both the field of nonlinear dynamics and non-smooth mechanics, presenting a framework for a class of non-smooth mechanical systems using techniques from both fields. The book reviews recent developments, and opens the field to the nonlinear dynamics community. This book addresses researchers and graduate students in engineering and mathematics interested in the modelling, simulation and dynamics of non-smooth systems and nonlinear dynamics.

Dynamics and Bifurcations of Non-Smooth Mechanical Systems

Dynamics and Bifurcations of Non-Smooth Mechanical Systems PDF Author: Remco Leine
Publisher: Springer Science & Business Media
ISBN: 9783540219873
Category : Mathematics
Languages : en
Pages : 252

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Book Description
This monograph combines the knowledge of both the field of nonlinear dynamics and non-smooth mechanics, presenting a framework for a class of non-smooth mechanical systems using techniques from both fields. The book reviews recent developments, and opens the field to the nonlinear dynamics community. This book addresses researchers and graduate students in engineering and mathematics interested in the modelling, simulation and dynamics of non-smooth systems and nonlinear dynamics.

Dynamics and Bifurcations of Non-Smooth Mechanical Systems

Dynamics and Bifurcations of Non-Smooth Mechanical Systems PDF Author: Remco I. Leine
Publisher: Springer Science & Business Media
ISBN: 3540443983
Category : Mathematics
Languages : en
Pages : 245

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Book Description
This monograph combines the knowledge of both the field of nonlinear dynamics and non-smooth mechanics, presenting a framework for a class of non-smooth mechanical systems using techniques from both fields. The book reviews recent developments, and opens the field to the nonlinear dynamics community. This book addresses researchers and graduate students in engineering and mathematics interested in the modelling, simulation and dynamics of non-smooth systems and nonlinear dynamics.

Dynamics and Bifurcations of Non-Smooth Mechanical Systems

Dynamics and Bifurcations of Non-Smooth Mechanical Systems PDF Author: Remco Leine
Publisher: Springer
ISBN: 9783642535796
Category : Mathematics
Languages : en
Pages : 236

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Book Description
This monograph combines the knowledge of both the field of nonlinear dynamics and non-smooth mechanics, presenting a framework for a class of non-smooth mechanical systems using techniques from both fields. The book reviews recent developments, and opens the field to the nonlinear dynamics community. This book addresses researchers and graduate students in engineering and mathematics interested in the modelling, simulation and dynamics of non-smooth systems and nonlinear dynamics.

Bifurcation and Chaos in Nonsmooth Mechanical Systems

Bifurcation and Chaos in Nonsmooth Mechanical Systems PDF Author: Jan Awrejcewicz
Publisher: World Scientific
ISBN: 9812384596
Category : Science
Languages : en
Pages : 564

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Book Description
This book presents the theoretical frame for studying lumped nonsmooth dynamical systems: the mathematical methods are recalled, and adapted numerical methods are introduced (differential inclusions, maximal monotone operators, Filippov theory, Aizerman theory, etc.). Tools available for the analysis of classical smooth nonlinear dynamics (stability analysis, the Melnikov method, bifurcation scenarios, numerical integrators, solvers, etc.) are extended to the nonsmooth frame. Many models and applications arising from mechanical engineering, electrical circuits, material behavior and civil engineering are investigated to illustrate theoretical and computational developments.

Non-smooth Problems in Vehicle Systems Dynamics

Non-smooth Problems in Vehicle Systems Dynamics PDF Author: Per Grove Thomsen
Publisher: Springer Science & Business Media
ISBN: 3642013562
Category : Technology & Engineering
Languages : en
Pages : 262

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Book Description
The book combines vehicle systems dynamics with the latest theoretical developments in dynamics of non-smooth systems and numerical analysis of differential-algebraic dynamical systems with discontinuities. These two fields are fundamental for the modelling and analysis of vehicle dynamical sytems. The results are also applicable to other non-smooth dynamical systems.

Bifurcation and Chaos in Nonsmooth Mechanical Systems

Bifurcation and Chaos in Nonsmooth Mechanical Systems PDF Author: Jan Awrejcewicz
Publisher: World Scientific
ISBN: 9789812564801
Category : Mathematics
Languages : en
Pages : 566

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Book Description
This book presents the theoretical frame for studying lumped nonsmoothdynamical systems: the mathematical methods are recalled, and adaptednumerical methods are introduced (differential inclusions, maximalmonotone operators, Filippov theory, Aizerman theory, etc.

Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields

Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields PDF Author: John Guckenheimer
Publisher: Springer Science & Business Media
ISBN: 1461211409
Category : Mathematics
Languages : en
Pages : 475

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Book Description
An application of the techniques of dynamical systems and bifurcation theories to the study of nonlinear oscillations. Taking their cue from Poincare, the authors stress the geometrical and topological properties of solutions of differential equations and iterated maps. Numerous exercises, some of which require nontrivial algebraic manipulations and computer work, convey the important analytical underpinnings of problems in dynamical systems and help readers develop an intuitive feel for the properties involved.

Piecewise-smooth Dynamical Systems

Piecewise-smooth Dynamical Systems PDF Author: Mario Bernardo
Publisher: Springer Science & Business Media
ISBN: 1846287081
Category : Mathematics
Languages : en
Pages : 497

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Book Description
This book presents a coherent framework for understanding the dynamics of piecewise-smooth and hybrid systems. An informal introduction expounds the ubiquity of such models via numerous. The results are presented in an informal style, and illustrated with many examples. The book is aimed at a wide audience of applied mathematicians, engineers and scientists at the beginning postgraduate level. Almost no mathematical background is assumed other than basic calculus and algebra.

Oscillators and Oscillatory Signals from Smooth to Discontinuous

Oscillators and Oscillatory Signals from Smooth to Discontinuous PDF Author: Valery N. Pilipchuk
Publisher: Springer Nature
ISBN: 3031377885
Category : Science
Languages : en
Pages : 461

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Book Description
This updated and enriched new edition maintains its complementarity principle in which the subgroup of rotations, harmonic oscillators, and the conventional complex analysis generate linear and weakly nonlinear approaches, whereas translations and reflections, impact oscillators, and hyperbolic Clifford’s algebras, give rise to the essentially nonlinear “quasi-impact” methodology based on the idea of non-smooth temporal substitutions. In the years since “Nonlinear Dynamics: Between Linear and Impact Limits,” the previous edition of this book, was published, due to a widening area of applications, a deeper insight into the matter has emerged leading to the rudimentary algebraic view on the very existence of the complementary smooth and non-smooth base systems as those associated with two different signs of the algebraic equation j2 =± 1. This edition further includes an overview of applications found in the literature after the publication of first edition, and new physical examples illustrating both theoretical statements and constructive analytical tools.

Nonsmooth Mechanics and Convex Optimization

Nonsmooth Mechanics and Convex Optimization PDF Author: Yoshihiro Kanno
Publisher: CRC Press
ISBN: 1420094238
Category : Science
Languages : en
Pages : 447

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Book Description
"This book concerns matter that is intrinsically difficult: convex optimization, complementarity and duality, nonsmooth analysis, linear and nonlinear programming, etc. The author has skillfully introduced these and many more concepts, and woven them into a seamless whole by retaining an easy and consistent style throughout. The book is not all theory: There are many real-life applications in structural engineering, cable networks, frictional contact problems, and plasticity... I recommend it to any reader who desires a modern, authoritative account of nonsmooth mechanics and convex optimization." — Prof. Graham M.L. Gladwell, Distinguished Professor Emeritus, University of Waterloo, Fellow of the Royal Society of Canada "... reads very well—the structure is good, the language and style are clear and fluent, and the material is rendered accessible by a careful presentation that contains many concrete examples. The range of applications, particularly to problems in mechanics, is admirable and a valuable complement to theoretical and computational investigations that are at the forefront of the areas concerned." — Prof. B. Daya Reddy, Department of Mathematics and Applied Mathematics, Director of Centre for Research in Computational and Applied Mechanics, University of Cape Town, South Africa "Many materials and structures (e.g., cable networks, membrane) involved in practical engineering applications have complex responses that cannot be described by smooth constitutive relations. ... The author shows how these difficult problems can be tackled in the framework of convex analysis by arranging the carefully chosen materials in an elegant way. Most of the contents of the book are from the original contributions of the author. They are both mathematically rigorous and readable. This book is a must-read for anyone who intends to get an authoritative and state-of-art description for the analysis of nonsmooth mechanics problems with theory and tools from convex analysis." — Prof. Xu Guo, State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics, Dalian University of Technology