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The World of Coupled Nonlinear Oscillators

  • Hermann Haken
Part of the Springer Series in Synergetics book series (SSSYN, volume 20)

Abstract

When speaking of oscillators, probably most of us first think of mechanical oscillators such as springs. Another example from mechanics is provided by the pendulum. It can be treated as a linear oscillator if its amplitude of oscillation is small enough, but otherwise it represents a nonlinear oscillator. In many cases of practical importance we have to deal with coupled oscillators. For instance, think of a piece of elastic material which for mathematical treatment is treated as a set of coupled finite elements each of which can be represented as an oscillator. Such methods are of great importance in mechanical engineering, for instance when dealing with vibrations of engines or towers, or with flutter of wings of airplanes. Of course, in a number of cases we consider the limiting case in which the finite elements approach a continuous distribution which corresponds to our original picture of an elastic medium. Oscillations occur equally well in electrical and radio engineering. Here we deal not only with the old radio tube oscillator but with modern circuits using transistors and other electronic devices.

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Bibliography

  1. This section gives only a sketch, for detailed treatments of nonlinear oscillators see N. N. Bogoliubov, Y. A. Mitropolsky: Asymptotic Methods in the Theory of Nonlinear Oscillations (Hindustan Publ. Corp., New Delhi 1961)Google Scholar
  2. N. Minorski: Nonlinear Oscillations (Van Nostrand, Toronto 1962)Google Scholar
  3. A. Andronov, A. Vitt, S. E. Khaikin: Theory of Oscillators (Pergamon, London 1966)zbMATHGoogle Scholar
  4. N. N. Bogoliubov, I. A. Mitropolskii, A. M. Samoilento: Methods of Accelerated Convergence in Nonlinear Mechanics (Springer, Berlin, Heidelberg, New York 1976)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1983

Authors and Affiliations

  • Hermann Haken
    • 1
  1. 1.Institut für Theoretische PhysikUniversität StuttgartStuttgart 80Fed. Rep. of Germany

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