Nonlinear Autonomous Oscillations: Analytical Theory
eBook - PDF

Nonlinear Autonomous Oscillations: Analytical Theory

  1. 329 pages
  2. English
  3. PDF
  4. Available on iOS & Android
eBook - PDF

Nonlinear Autonomous Oscillations: Analytical Theory

About this book

Nonlinear Autonomous Oscillations presents a self-contained and readable account for mathematicians, physicists, and engineers. This monograph is mainly concerned with the analytical theory of nonlinear autonomous oscillations, with the approach based mostly on the author's work. After some introductory material, in Chapter 5 a moving orthogonal coordinate system along a closed orbit is introduced. In the next four chapters, stability theory and perturbation theory are systematically discussed for general autonomous systems by means of a moving coordinate system. In Chapter 10, the two-dimensional autonomous system is discussed in detail on the basis of results obtained in the preceding chapters. In Chapter 11, a numerical method for determining a periodic solution of the general nonlinear autonomous system is described. To illustrate this, the periodic solutions of the autonomous van der Pol equation for various values of thedamping coefficient are computed. Chapter 12, which is based on the work of the author and Sibuya, discusses the center of higher dimension. Chapter 13 discusses a particular inverse problem connected with the period of periodicsolutions of one interesting equation. There are, of course, many other topics of importance in the theory of nonlinear autonomous oscillations. These are, however, omitted in the present monograph because they are mainly topological rather than analytical and in order to keep the book from growing inordinately long.

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Yes, you can access Nonlinear Autonomous Oscillations: Analytical Theory by Urabe in PDF and/or ePUB format, as well as other popular books in Computer Science & Computer Science General. We have over one million books available in our catalogue for you to explore.

Table of contents

  1. Front Cover
  2. Nonlinear Autonomous Oscillations
  3. Copyright Page
  4. Contents
  5. Preface
  6. Chapter 1. Analysis of Vectors and Matrices
  7. Chapter 2. Basic Theorems Concerning Ordinary Differential Equations
  8. Chapter 3. Linear Differential Systems
  9. Chapter 4. Orbits of Autonomous Systems
  10. Chapter 5. Moving Orthonormal Systems along a Closed Orbit
  11. Chapter 6. Stability
  12. Chapter 7. Perturbation of Autonomous Systems
  13. Chapter 8. Perturbation of Fully Oscillatory Systems
  14. Chapter 9. Perturbation of Partially Oscillatory Systems
  15. Chapter 10. Analysis of Two-Dimensional Autonomous Systems
  16. Chapter 11. Numerical Computation of Periodic Solutions
  17. Chapter 12. Center of the Autonomous System
  18. Chapter 13. Inverse Problems Connected with Periods of Oscillations Described by x + g(x) = 0
  19. Appendix. The Newton Method and Step-by-Step Methods for Ordinary Differential Equations
  20. Bibliography
  21. Subject Index