Screen LibraryNonlinear dynamics of piecewise constant systems and implementation of piecewise constant arguments /
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 co...
Saved in:
| Main Authors: | |
|---|---|
| Corporate Authors: | |
| Published: |
World Scientific Pub. Co.,
|
| Publisher Address: | Singapore : |
| Publication Dates: | 2008. |
| Literature type: | eBook |
| Language: | English |
| Subjects: | |
| Online Access: |
http://www.worldscientific.com/worldscibooks/10.1142/6882#t=toc |
| Summary: |
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 the 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. |
| Carrier Form: | 1 online resource (xvi,328pages) : illustrations (some color) |
| Bibliography: | Includes bibliographical references and index. |
| ISBN: | 9789812818515 (electronic bk.) |
| CLC: | O31 |
| Contents: | ch. 1. Fundamentals of conventional and piecewise constant systems. 1.1. Preliminary remarks. 1.2. Remarks on the development and analyses of piecewise constant systems in history. 1.3. Modeling and analysis procedures for conventional continuous and piecewise constant systems. 1.4. Fundamentals of dynamic system modeling in science and engineering. 1.5. Piecewise constant systems and their modeling. 1.6. Implementing piecewise constant arguments in dynamic problem solving -- ch. 2. Preliminary theorems and techniques for analysis of nonlinear piecewise constant systems. 2.1. Introduction. 2.2. Nonlinear behaviors and fundamental analytical and geometric tools of nonlinear dynamics. 2.3. Lyapunov exponent. 2.4. Characteristics of numerical solutions and Runge-Kutta method -- ch. 3. Piecewise constant dynamical systems and their behavior. 3.1. Introduction. 3.2. Governing equations of dynamic systems with piecewise constant variables. 3.3. Solution development of simple dynamic systems subjected to piecewise constant excitations. 3.4. Development of analytical solutions via piecewise constant variables. 3.5. General vibration systems under piecewise constant excitations. 3.6. Derivation and characteristics of approximate and numerical solutions of dynamic systems with piecewise constant variables. 3.7. Extraordinary and nonlinear behavior of linear piecewise constant systems. 3.8. Oscillatory properties of dynamic systems with piecewise constant variables. 3.9. Approximate and numerical technique of small interval with piecewise constant variable. 3.10. Characteristics of approximate results with piecewise constant variable in small intervals -- ch. 4. Analytical and semi-analytical solution development with piecewise constant arguments. 4.1. Introduction. 4.2. A new piecewise constant argument [symbol]. 4.3. Solving for dynamic systems with implementation of piecewise constant arguments. 4.4. Analytical solutions of free vibration systems via piecewise constantization. 4.5. Analytical solutions to undamped systems with piecewise constant excitations. 4.6. Development of general analytical solutions for linear vibration systems. 4.7. Semi-analytical and approximate solutions for nonlinear piecewise constant dynamic systems -- ch. 5. Numerical and improved semi-analytical approaches implementing piecewise constant arguments. 5.1. Introduction. 5.2. Numerical solutions for linear dynamic systems via piecewise constant procedure. 5.3. Numerical solutions of nonlinear systems. 5.4. Chaotic behavior of numerical solutions for nonlinear systems. 5.5. Development of P-T method. 5.6. Analytical and numerical approaches and the approaches implementing P-T method. 5.7. Numerical solution comparison between P-T and Runge-Kutta methods. 5.8. Consistency analysis of numerical solutions with implementation of piecewise constant arguments. 5.9. Step size control. 5.10. Characteristics of the P-T method -- ch. 6. Application of P-T method on multi-degree-of-freedom nonlinear dynamic systems. 6.1. Introduction. 6.2. Existing approaches for solving multi-degree-of-freedom linear and nonlinear dynamic systems. 6.3. Derivation of general nonlinear MDOF dynamic systems with piecewise constant arguments. 6.4. Numerical solutions via piecewise constantization -- ch. 7. Periodicity-Ratio and its application in diagnosing irregularities of nonlinear systems. 7.1. Introduction. 7.2. Phase trajectories of periodic, nonperiodic and chaotic behavior of nonlinear systems. 7.3. Poincare Maps and their relation with piecewise constant dynamic systems. 7.4. Bifurcation of piecewise constant dynamic systems. 7.5. Derivation of Periodicity-Ratio. 7.6. Distinction of quasiperiodic motion from chaos. 7.7. Comparison of Periodicity-Ratio and Lyapunov-Exponent. 7.8. Characteristics of Periodicity-Ratio. 7.9. Implementation of Periodicity-Ratio in analyzing nonlinear dynamic problems. |