Computational Methods For Nonlinear Dynamical Systems

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Computational Methods For Nonlinear Dynamical Systems

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Author : Xuechuan Wang
language : en
Publisher: Elsevier
Release Date : 2022-09-28

Computational Methods For Nonlinear Dynamical Systems written by Xuechuan Wang and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-09-28 with Mathematics categories.

Computational Methods for Nonlinear Dynamical Systems: Theory and Applications in Aerospace Engineering proposes novel ideas and develops highly-efficient and accurate methods for solving nonlinear dynamic systems, drawing inspiration from the weighted residual method and the asymptotic method. Proposed methods can be used both for real-time simulation and the analysis of nonlinear dynamics in aerospace engineering. The book introduces global estimation methods and local computational methods for nonlinear dynamic systems. Starting from the classic asymptotic, finite difference and weighted residual methods, typical methods for solving nonlinear dynamic systems are considered. In addition, new high-performance methods are proposed, such as time-domain collocation and local variational iteration. The book summarizes and develops computational methods for strongly nonlinear dynamic systems and considers the practical application of the methods within aerospace engineering. Presents global methods for solving periodic nonlinear dynamical behaviors Gives local methods for solving transient nonlinear responses Outlines computational methods for linear, nonlinear, ordinary and partial differential equations Emphasizes the development of accurate and efficient numerical methods that can be used in real-world missions Reveals practical applications of methods through orbital mechanics and structural dynamics

Applied Nonlinear Dynamics

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Author : Ali H. Nayfeh
language : en
Publisher: John Wiley & Sons
Release Date : 2008-11-20

Applied Nonlinear Dynamics written by Ali H. Nayfeh and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-11-20 with Science categories.

A unified and coherent treatment of analytical, computational and experimental techniques of nonlinear dynamics with numerous illustrative applications. Features a discourse on geometric concepts such as Poincaré maps. Discusses chaos, stability and bifurcation analysis for systems of differential and algebraic equations. Includes scores of examples to facilitate understanding.

Nonlinear Systems Vol 1

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Author : Victoriano Carmona
language : en
Publisher: Springer
Release Date : 2018-09-15

Nonlinear Systems Vol 1 written by Victoriano Carmona and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-09-15 with Science categories.

This book is part of a two volume set which presents the analysis of nonlinear phenomena as a long-standing challenge for research in basic and applied science as well as engineering. It discusses nonlinear differential and differential equations, bifurcation theory for periodic orbits and global connections. The integrability and reversibility of planar vector fields and theoretical analysis of classic physical models are sketched. This first volume concentrates on the mathematical theory and computational techniques that are essential for the study of nonlinear science, a second volume deals with real-world nonlinear phenomena in condensed matter, biology and optics.

Dynamical Systems And Numerical Analysis

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Author : Andrew Stuart
language : en
Publisher: Cambridge University Press
Release Date : 1998-11-28

Dynamical Systems And Numerical Analysis written by Andrew Stuart and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-11-28 with Mathematics categories.

The first three chapters contain the elements of the theory of dynamical systems and the numerical solution of initial-value problems. In the remaining chapters, numerical methods are formulated as dynamical systems and the convergence and stability properties of the methods are examined.

Perspectives Of Nonlinear Dynamics Volume 2

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Author : E. Atlee Jackson
language : en
Publisher: CUP Archive
Release Date : 1989

Perspectives Of Nonlinear Dynamics Volume 2 written by E. Atlee Jackson and has been published by CUP Archive this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Mathematics categories.

The dynamics of physical, chemical, biological or fluid systems generally must be described by nonlinear models, whose detailed mathematical solutions are not obtainable. To understand some aspects of such dynamics, various complementary methods and viewpoints are of crucial importance. The presentation and style is intended to stimulate the reader's imagination to apply these methods to a host of problems and situations.

Dynamical Systems

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Author : Mahmut Reyhanoglu
language : en
Publisher: BoD – Books on Demand
Release Date : 2017-03-15

Dynamical Systems written by Mahmut Reyhanoglu and has been published by BoD – Books on Demand this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-03-15 with Mathematics categories.

There has been a considerable progress made during the recent past on mathematical techniques for studying dynamical systems that arise in science and engineering. This progress has been, to a large extent, due to our increasing ability to mathematically model physical processes and to analyze and solve them, both analytically and numerically. With its eleven chapters, this book brings together important contributions from renowned international researchers to provide an excellent survey of recent advances in dynamical systems theory and applications. The first section consists of seven chapters that focus on analytical techniques, while the next section is composed of four chapters that center on computational techniques.

Numerical Methods For Nonsmooth Dynamical Systems

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Author : Vincent Acary
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-01-30

Numerical Methods For Nonsmooth Dynamical Systems written by Vincent Acary 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 2008-01-30 with Technology & Engineering categories.

This book concerns the numerical simulation of dynamical systems whose trajec- ries may not be differentiable everywhere. They are named nonsmooth dynamical systems. They make an important class of systems, rst because of the many app- cations in which nonsmooth models are useful, secondly because they give rise to new problems in various elds of science. Usually nonsmooth dynamical systems are represented as differential inclusions, complementarity systems, evolution va- ational inequalities, each of these classes itself being split into several subclasses. The book is divided into four parts, the rst three parts being sketched in Fig. 0. 1. The aim of the rst part is to present the main tools from mechanics and applied mathematics which are necessary to understand how nonsmooth dynamical systems may be numerically simulated in a reliable way. Many examples illustrate the th- retical results, and an emphasis is put on mechanical systems, as well as on electrical circuits (the so-called Filippov’s systems are also examined in some detail, due to their importance in control applications). The second and third parts are dedicated to a detailed presentation of the numerical schemes. A fourth part is devoted to the presentation of the software platform Siconos. This book is not a textbook on - merical analysis of nonsmooth systems, in the sense that despite the main results of numerical analysis (convergence, order of consistency, etc. ) being presented, their proofs are not provided.

Computational Methods In Nonlinear Structural And Solid Mechanics

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Author : Ahmed K. Noor
language : en
Publisher: Elsevier
Release Date : 2014-05-20

Computational Methods In Nonlinear Structural And Solid Mechanics written by Ahmed K. Noor and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-20 with Mathematics categories.

Computational Methods in Nonlinear Structural and Solid Mechanics covers the proceedings of the Symposium on Computational Methods in Nonlinear Structural and Solid Mechanics. The book covers the development of efficient discretization approaches; advanced numerical methods; improved programming techniques; and applications of these developments to nonlinear analysis of structures and solids. The chapters of the text are organized into 10 parts according to the issue they tackle. The first part deals with nonlinear mathematical theories and formulation aspects, while the second part covers computational strategies for nonlinear programs. Part 3 deals with time integration and numerical solution of nonlinear algebraic equations, while Part 4 discusses material characterization and nonlinear fracture mechanics, and Part 5 tackles nonlinear interaction problems. The sixth part discusses seismic response and nonlinear analysis of concrete structure, and the seventh part tackles nonlinear problems for nuclear reactors. Part 8 covers crash dynamics and impact problems, while Part 9 deals with nonlinear problems of fibrous composites and advanced nonlinear applications. The last part discusses computerized symbolic manipulation and nonlinear analysis software systems. The book will be of great interest to numerical analysts, computer scientists, structural engineers, and other professionals concerned with nonlinear structural and solid mechanics.

Computational Methods In Bifurcation Theory And Dissipative Structures

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Author : M. Kubicek
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Computational Methods In Bifurcation Theory And Dissipative Structures written by M. Kubicek 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 2012-12-06 with Science categories.

"Dissipative structures" is a concept which has recently been used in physics to discuss the formation of structures organized in space and/or time at the expense of the energy flowing into the system from the outside. The space-time structural organization of biological systems starting from the subcellular level up to the level of ecological systems, coherent structures in laser and of elastic stability in mechanics, instability in hydro plasma physics, problems dynamics leading to the development of turbulence, behavior of electrical networks and chemical reactors form just a short list of problems treated in this framework. Mathematical models constructed to describe these systems are usually nonlinear, often formed by complicated systems of algebraic, ordinary differ ential, or partial differential equations and include a number of character istic parameters. In problems of theoretical interest as well as engineering practice, we are concerned with the dependence of solutions on parameters and particularly with the values of parameters where qualitatively new types of solutions, e.g., oscillatory solutions, new stationary states, and chaotic attractors, appear (bifurcate). Numerical techniques to determine both bifurcation points and the depen dence of steady-state and oscillatory solutions on parameters are developed and discussed in detail in this text. The text is intended to serve as a working manual not only for students and research workers who are interested in dissipative structures, but also for practicing engineers who deal with the problems of constructing models and solving complicated nonlinear systems.

Nonlinear Systems

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Author : Victoriano Carmona
language : en
Publisher:
Release Date : 2018

Nonlinear Systems written by Victoriano Carmona and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with Nonlinear systems categories.

This book is part of a two volume set which presents the analysis of nonlinear phenomena as a long-standing challenge for research in basic and applied science as well as engineering. It discusses nonlinear differential and differential equations, bifurcation theory for periodic orbits and global connections. The integrability and reversibility of planar vector fields and theoretical analysis of classic physical models are sketched. This first volume concentrates on the mathematical theory and computational techniques that are essential for the study of nonlinear science, a second volume deals with real-world nonlinear phenomena in condensed matter, biology and optics.