A Smooth and Discontinuous Oscillator : Theory, Methodology and Applications

Alain Léger

ISBN 10: 3662571102 / ISBN 13: 9783662571101

Verlag: Springer Berlin Heidelberg, 2018

Beschreibung

Druck auf Anfrage Neuware - Printed after ordering - 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.

Bestandsnummer des Verkäufers 9783662571101

Bibliografische Details

• Titel: A Smooth and Discontinuous Oscillator : Theory, Methodology and Applications
• Verlag: Springer Berlin Heidelberg
• Erscheinungsjahr: 2018
• Sprache: Englisch
• ISBN-10: 3662571102
• ISBN-13: 9783662571101
• Einband: Taschenbuch
• Zustand: Neu
• Abmessungen: 235B x 155 H x 16 T Millimeter Breite: 235 mm, Höhe: 155 mm, Tiefe: 16 mm
• Gewicht: 435 Gramm

Über diesen Titel

Inhaltsangabe

Clearly illustrates the nature of nonlinear phenomena by introducing a real mechanical model, the SD oscillator, which offers an effectives model for describing geometrical nonlinearities

Opens a new perspective on the inner workings of the real world through this simple actual mechanical model without any truncation

Offers an opportunity to broaden our conventional nonlinear understanding to the unconventional nonlinear systems with applications in engineering and interdisciplinary areas

Von der hinteren Coverseite

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 th

e 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.