نوسانات خودکار غیرخطی؛ نظریه تحلیلی، جلد ۳۴

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. Content: Edited by Page v Copyright page Page vi Preface Pages vii-viii Minoru Urabb 1. Analysis of Vectors and Matrices Pages 1-16 2. Basic Theorems Concerning Ordinary Differential Equations Pages 17-23 3. Linear Differential Systems Pages 24-33 4. Orbits of Autonomous Systems Pages 34-41 5. Moving Orthonormal Systems along a Closed Orbit Pages 42-53 6. Stability Pages 54-90 7. Perturbation of Autonomous Systems Pages 91-100 8. Perturbation of Fully Oscillatory Systems Pages 101-118 9. Perturbation of Partially Oscillatory Systems Pages 119-162 10. Analysis of Two-Dimensional Autonomous Systems Pages 163-203 11. Numerical Computation of Periodic Solutions Pages 204-228 12. Center of the Autonomous System Pages 229-243 13. Inverse Problems Connected with Periods of Oscillations Described by + g(x) = 0 Pages 244-279 Appendix: The Newton Method and Step-by-Step Methods for Ordinary Differential Equations Pages 280-322 Bibliography Review Article Pages 323-325 Subject Index Pages 327-330