A Smooth And Discontinuous Oscillator

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A Smooth And Discontinuous Oscillator

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Author : Qingjie Cao
language : en
Publisher: Springer
Release Date : 2016-09-27

A Smooth And Discontinuous Oscillator written by Qingjie Cao and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-09-27 with Technology & Engineering categories.

This is the first book to introduce the irrational elliptic function series, providing a theoretical treatment for the smooth and discontinuous system and opening a new branch of applied mathematics. The discovery of the smooth and discontinuous (SD) oscillator and the SD attractors discussed in this book represents a further milestone in nonlinear dynamics, following on the discovery of the Ueda attractor in 1961 and Lorenz attractor in 1963. This particular system bears significant similarities to the Duffing oscillator, exhibiting the standard dynamics governed by the hyperbolic structure associated with the stationary state of the double well. However, there is a substantial departure in nonlinear dynamics from standard dynamics at the discontinuous stage. The constructed irrational elliptic function series, which offers a way to directly approach the nature dynamics analytically for both smooth and discontinuous behaviours including the unperturbed periodic motions and the perturbed chaotic attractors without any truncation, is of particular interest. Readers will also gain a deeper understanding of the actual nonlinear phenomena by means of a simple mechanical model: the theory, methodology, and the applications in various interlinked disciplines of sciences and engineering. This book offers a valuable resource for researchers, professionals and postgraduate students in mechanical engineering, non-linear dynamics, and related areas, such as nonlinear modelling in various fields of mathematics, physics and the engineering sciences.

Oscillators And Oscillatory Signals From Smooth To Discontinuous

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Author : Valery N. Pilipchuk
language : en
Publisher: Springer Nature
Release Date : 2023-09-23

Oscillators And Oscillatory Signals From Smooth To Discontinuous written by Valery N. Pilipchuk and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-09-23 with Science categories.

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.

Qualitative Analysis Of Nonsmooth Dynamics

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Author : Alain Léger
language : en
Publisher: Elsevier
Release Date : 2016-04-26

Qualitative Analysis Of Nonsmooth Dynamics written by Alain Léger and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-04-26 with Technology & Engineering categories.

Qualitative Analysis of Nonsmooth Dynamics: A Simple Discrete System with Unilateral Contact and Coulomb Friction explores the effects of small and large deformations to understand how shocks, sliding, and stick phases affect the trajectories of mechanical systems. By analyzing these non-regularities successively this work explores the set of equilibria and properties of periodic solutions of elementary mechanical systems, where no classical results issued from the theory of ordinary differential equations are readily available, such as stability, continuation or approximation of solutions. The authors focus on unilateral contact in presence of Coulomb friction and show, in particular, how any regularization would greatly simplify the mathematics but lead to unacceptable physical responses. - Explores the effects of small and large deformations to understand how shocks, sliding, and stick phases affect the trajectories of mechanical systems - Includes theoretical results concerning the full investigation of the behavior under constant or oscillating loadings, even in the case of the simplest mechanical systems - Provides a focus on unilateral contact in presence of Coulomb friction - Helps you gain an accurate understanding of how the transition occurs to ensure the safe use of any machine involving rotating or sliding mechanisms

Research And Applications In Structural Engineering Mechanics And Computation

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Author : Alphose Zingoni
language : en
Publisher: CRC Press
Release Date : 2013-08-15

Research And Applications In Structural Engineering Mechanics And Computation written by Alphose Zingoni and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-08-15 with Science categories.

Research and Applications in Structural Engineering, Mechanics and Computation contains the Proceedings of the Fifth International Conference on Structural Engineering, Mechanics and Computation (SEMC 2013, Cape Town, South Africa, 2-4 September 2013). Over 420 papers are featured. Many topics are covered, but the contributions may be seen to fall

Real And Complex Dynamical Systems

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Author : B. Branner
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14

Real And Complex Dynamical Systems written by B. Branner and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Mathematics categories.

This volume contains edited versions of 11 contributions given by main speakers at the NATO Advanced Study Institute on lReal and Complex Dynamical Systems in Hiller0d, Denmark, June 20th - July 2nd, 1993. The vision of the institute was to illustrate the interplay between two important fields of Mathematics: Real Dynamical Systems and Complex Dynamical Systems. The interaction between these two fields has been growing over the years. Problems in Real Dynamical Systems have recently been solved using complex tools in the real or by extension to the complex. In return, problems in Complex Dynamical Systems have been settled using results from Real Dynamical Systems. The programme of the institute was to examine the state of the art of central parts of both Real and Complex Dynamical Systems, to reinforce contact between the two aspects of the theory and to make recent progress in each accessible to a larger group of mathematicians.

Non Smooth Problems In Vehicle Systems Dynamics

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Author : Per Grove Thomsen
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-11-09

Non Smooth Problems In Vehicle Systems Dynamics written by Per Grove Thomsen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-11-09 with Technology & Engineering categories.

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 In Autonomous And Nonautonomous Differential Equations With Discontinuities

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Author : Marat Akhmet
language : en
Publisher: Springer
Release Date : 2017-01-23

Bifurcation In Autonomous And Nonautonomous Differential Equations With Discontinuities written by Marat Akhmet and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-01-23 with Mathematics categories.

This book focuses on bifurcation theory for autonomous and nonautonomous differential equations with discontinuities of different types – those with jumps present either in the right-hand side, or in trajectories or in the arguments of solutions of equations. The results obtained can be applied to various fields, such as neural networks, brain dynamics, mechanical systems, weather phenomena and population dynamics. Developing bifurcation theory for various types of differential equations, the book is pioneering in the field. It presents the latest results and provides a practical guide to applying the theory to differential equations with various types of discontinuity. Moreover, it offers new ways to analyze nonautonomous bifurcation scenarios in these equations. As such, it shows undergraduate and graduate students how bifurcation theory can be developed not only for discrete and continuous systems, but also for those that combine these systems in very different ways. At the same time, it offers specialists several powerful instruments developed for the theory of discontinuous dynamical systems with variable moments of impact, differential equations with piecewise constant arguments of generalized type and Filippov systems.

Discontinuous Dynamics And System Synchronization

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Author : Fuhong Min
language : en
Publisher: Springer Nature
Release Date : 2024-08-11

Discontinuous Dynamics And System Synchronization written by Fuhong Min and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-08-11 with Science categories.

This book provides a systematic introduction to the dynamical behaviors of discontinuous dynamical systems and system synchronization. The first part of the book presents the theory of flow switching in discontinuous dynamical systems as well as the switching dynamics in such discontinuous systems. The second part presents a theory for interaction discontinuities between distinct dynamical systems, from which partial and complete chaotic synchronizations in such systems are studied analytically and experimentally.

Global Nonlinear Dynamics For Engineering Design And System Safety

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Author : Stefano Lenci
language : en
Publisher: Springer
Release Date : 2018-09-24

Global Nonlinear Dynamics For Engineering Design And System Safety written by Stefano Lenci and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-09-24 with Technology & Engineering categories.

This is the first book which exploits concepts and tools of global nonlinear dynamics for bridging the gap between theoretical and practical stability of systems/structures, and for possibly enhancing the engineering design in macro-, micro- and nano-mechanics. Addressed topics include complementing theoretical and practical stability to achieve load carrying capacity; dynamical integrity for analyzing global dynamics, for interpreting/predicting experimental behavior, for getting hints towards engineering design; techniques for control of chaos; response of uncontrolled and controlled system/models in applied mechanics and structural dynamics by also considerung the effect of system imperfections; from relatively simple systems to multidimensional models representative of real world applications; potential and expected impact of global dynamics for engineering design.

Poincar Andronov Melnikov Analysis For Non Smooth Systems

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Author : Michal Feckan
language : en
Publisher: Academic Press
Release Date : 2016-06-07

Poincar Andronov Melnikov Analysis For Non Smooth Systems written by Michal Feckan and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-06-07 with Mathematics categories.

Poincaré-Andronov-Melnikov Analysis for Non-Smooth Systems is devoted to the study of bifurcations of periodic solutions for general n-dimensional discontinuous systems. The authors study these systems under assumptions of transversal intersections with discontinuity-switching boundaries. Furthermore, bifurcations of periodic sliding solutions are studied from sliding periodic solutions of unperturbed discontinuous equations, and bifurcations of forced periodic solutions are also investigated for impact systems from single periodic solutions of unperturbed impact equations. In addition, the book presents studies for weakly coupled discontinuous systems, and also the local asymptotic properties of derived perturbed periodic solutions. The relationship between non-smooth systems and their continuous approximations is investigated as well. Examples of 2-, 3- and 4-dimensional discontinuous ordinary differential equations and impact systems are given to illustrate the theoretical results. The authors use so-called discontinuous Poincaré mapping which maps a point to its position after one period of the periodic solution. This approach is rather technical, but it does produce results for general dimensions of spatial variables and parameters as well as the asymptotical results such as stability, instability, and hyperbolicity. - Extends Melnikov analysis of the classic Poincaré and Andronov staples, pointing to a general theory for freedom in dimensions of spatial variables and parameters as well as asymptotical results such as stability, instability, and hyperbolicity - Presents a toolbox of critical theoretical techniques for many practical examples and models, including non-smooth dynamical systems - Provides realistic models based on unsolved discontinuous problems from the literature and describes how Poincaré-Andronov-Melnikov analysis can be used to solve them - Investigates the relationship between non-smooth systems and their continuous approximations