A Smooth and Discontinuous Oscillator - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook A Smooth and Discontinuous Oscillator write by Qingjie Cao. This book was released on 2016-09-27. A Smooth and Discontinuous Oscillator available in PDF, EPUB and Kindle. 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
Oscillators and Oscillatory Signals from Smooth to Discontinuous - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Oscillators and Oscillatory Signals from Smooth to Discontinuous write by Valery N. Pilipchuk. This book was released on 2023-09-23. Oscillators and Oscillatory Signals from Smooth to Discontinuous available in PDF, EPUB and Kindle. 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.
Piecewise-smooth Dynamical Systems
Piecewise-smooth Dynamical Systems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Piecewise-smooth Dynamical Systems write by Mario Bernardo. This book was released on 2008-01-01. Piecewise-smooth Dynamical Systems available in PDF, EPUB and Kindle. 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.
Synchronization of Discontinuous Oscillators
Synchronization of Discontinuous Oscillators - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Synchronization of Discontinuous Oscillators write by Thomas Kirk Caughey. This book was released on 1952. Synchronization of Discontinuous Oscillators available in PDF, EPUB and Kindle.
Theory of Oscillators
Theory of Oscillators - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Theory of Oscillators write by A. A. Andronov. This book was released on 2013-10-22. Theory of Oscillators available in PDF, EPUB and Kindle. Theory of Oscillators presents the applications and exposition of the qualitative theory of differential equations. This book discusses the idea of a discontinuous transition in a dynamic process. Organized into 11 chapters, this book begins with an overview of the simplest type of oscillatory system in which the motion is described by a linear differential equation. This text then examines the character of the motion of the representative point along the hyperbola. Other chapters consider examples of two basic types of non-linear non-conservative systems, namely, dissipative systems and self-oscillating systems. This book discusses as well the discontinuous self-oscillations of a symmetrical multi-vibrator neglecting anode reaction. The final chapter deals with the immense practical importance of the stability of physical systems containing energy sources particularly control systems. This book is a valuable resource for electrical engineers, scientists, physicists, and mathematicians.
