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    Nonlinear Dynamics of Piecewise Consta. .

    ISBN-10: 9812818502
    ISBN-13: 9789812818508
    Author(s): Dai
    Description: "Piecewise constant systems exist in widely expanded areas such as engineering, physics, and mathematics. Extraordinary and complex characteristics of piecewise constant systems have been reported in recent years. This book provides the  More...
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    Publisher: World Scientific Publishing Company, Incorporated
    Binding: Hardcover
    Size: 6.25" wide x 9.00" long x 1.00" tall
    Weight: 1.342
    Language: English

    "Piecewise constant systems exist in widely expanded areas such as engineering, physics, and mathematics. Extraordinary and complex characteristics of piecewise constant systems have been reported in recent years. This book provides the methodologies for analyzing and assessing nonlinear piecewise constant systems on a theoretically and practically sound basis. Recently developed approaches for theoretically analyzing and numerically solving nonlinear piecewise constant dynamic systems are reviewed. A new greatest integer argument with a piecewise constant function is utilized for nonlinear dynamic analyses and for establishing a novel criterion in diagnosing irregular and chaotic solutions from the regular solutions of a nonlinear dynamic system. The newly established piecewise constantization methodology and its implementation in analytically solving for nonlinear dynamic problems are also presented."--BOOK JACKET.

    Preface
    Fundamentals of Conventional and Piecewise Constant Systems
    Preliminary Remarks
    Remarks on the Development and Analyses of Piecewise Constant Systems in History
    Modeling and Analysis Procedures for Conventional Continuous and Piecewise Constant Systems
    Fundamentals of Dynamic System Modeling in Science and Engineering
    Piecewise Constant Systems and Their Modeling
    Greatest Integer Functions
    Piecewise Constant System Modeling in Science and Engineering
    Implementing Piecewise Constant Arguments in Dynamic Problem Solving
    References
    Preliminary Theorems and Techniques for Analysis of Nonlinear Piecewise Constant Systems
    Introduction
    Nonlinear Behaviors and Fundamental Analytical and Geometric Tools of Nonlinear Dynamics
    Periodic Responses of Linear and Nonlinear Dynamic Systems
    Poincare Map
    Quasiperiodic Response of Nonlinear Systems
    Chaotic Response of Nonlinear Systems
    Bifurcation of Nonlinear Systems
    Lyapunov Exponent
    Characteristics of Numerical Solutions and Runge-Kutta Method
    References
    Piecewise Constant Dynamical Systems and Their Behavior
    Introduction
    Governing Equations of Dynamic Systems with Piecewise Constant Variables
    Solution Development of Simple Dynamic Systems Subjected to Piecewise Constant Excitations
    Development of Analytical Solutions via Piecewise Consant Variables
    General Vibration Systems under Piecewise Constant Excitations
    Derivation and Characteristics of Approximate and Numerical Solutions of Dynamic Systems with Piecewise Constant Variables
    Extraordinary and Nonlinear Behavior of Linear Piecewise Constant Systems
    Oscillatory Properties of Dynamic Systems with Piecewise Constant Variables
    Approximate and Numerical Technique of Small Interval with Piecewise Constant Variable
    Characteristics of Approximate Results with Piecewise Constant Variable in Small Intervals
    References
    Analytical and Semi-Analytical Solution Development with Piecewise Constant Arguments
    Introduction
    A New Piecewise Constant Argument [Nt]/N
    Solving for Dynamic Systems with Implementation of Piecewise Constant Arguments
    Analytical Solutions of Free Vibration Systems via Piecewise Constantization
    Analytical Solutions to Undamped Systems with Piecewise Constant Excitations
    Development of General Analytical Solutions for Linear Vibration Systems
    Semi-Analytical and Approximate Solutions for Nonlinear Piecewise Constant Dynamic Systems
    References
    Numerical and Improved Semi-Analytical Approaches Implementing Piecewise Constant Arguments
    Introduction
    Numerical Solutions for Linear Dynamic Systems via Piecewise Constant Procedure
    Numerical Solutions of Nonlinear Systems
    Chaotic Behavior of Numerical Solutions for Nonlinear Systems
    Development of P-T Method
    Analytical and Numerical Approaches and the Approaches Implementing P-T Method
    Numerical Solution Comparison between P-T and Runge-Kutta Methods
    Consistency Analysis of Numerical Solutions with Implementation of Piecewise Constant Arguments
    Step Size Control
    Characteristics of the P-T Method
    References
    Application of P-T Method on Multi-Degree-of-Freedom Nonlinear Dynamic Systems
    Introduction
    Existing Approaches for Solving Multi-Degree-of-Freedom Linear and Nonlinear Dynamic Systems
    Governing Equations and Solution Development of Linear MDOF Systems
    Solving for Nonlinear MDOF Systems
    Derivation of General Nonlinear MDOF Dynamic Systems with Piecewise Constant Arguments
    Solving Nonlinear Systems Directly Implementing P-T Method
    Nonlinear Systems with Linear Coupling and Proportional Damping
    Nonlinear Systems with Linear Coupling and General Damping
    Numerical Solutions via Piecewise Constantization
    References
    Periodicity-Ratio and Its Application in Diagnosing Irregularities of Nonlinear Systems
    Introduction
    Phase Trajectories of Periodic, Nonperiodic and Chaotic Behavior of Nonlinear Systems
    Poincare Maps and Their Relation with Piecewise Constant Dynamic Systems
    Bifurcation of Piecewise Constant Dynamic Systems
    Derivation of Periodicity-Ratio
    Distinction of Quasiperiodic Motion from Chaos
    Comparison of Periodicity-Ratio and Lyapunov-Exponent
    Characteristics of Periodicity-Ratio
    Implementation of Periodicity-Ratio in Analyzing Nonlinear Dynamic Problems
    References
    Mathematical Developments and Proofs
    Theory of Matrices
    Computer Programs for Analyses of Dynamics
    Index

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