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