Erschienen: 31.12.1995 Abbildung von Leonov / Burkin / Shepeljavyi | Frequency Methods in Oscillation Theory | 1995 | 357

Leonov / Burkin / Shepeljavyi

Frequency Methods in Oscillation Theory

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1995. Buch. xii, 404 S. Bibliographien. Hardcover

Springer. ISBN 978-0-7923-3896-3

Format (B x L): 16 x 24 cm

Gewicht: 888 g

In englischer Sprache

Das Werk ist Teil der Reihe: Mathematics and Its Applications; 357


The linear theory of oscillations traditionally operates with frequency representa­ tions based on the concepts of a transfer function and a frequency response. The universality of the critria of Nyquist and Mikhailov and the simplicity and obvi­ ousness of the application of frequency and amplitude - frequency characteristics in analysing forced linear oscillations greatly encouraged the development of practi­ cally important nonlinear theories based on various forms of the harmonic balance hypothesis [303]. Therefore mathematically rigorous frequency methods of investi­ gating nonlinear systems, which appeared in the 60s, also began to influence many areas of nonlinear theory of oscillations. First in this sphere of influence was a wide range of problems connected with multidimensional analogues of the famous van der Pol equation describing auto­ oscillations of generators of various radiotechnical devices. Such analogues have as a rule a unique unstable stationary point in the phase space and are Levinson dis­ sipative. One of the pioneering works in this field, which started the investigation of a three-dimensional analogue of the van der Pol equation, was K. O. Friedrichs's paper [123]. The author suggested a scheme for constructing a positively invariant set homeomorphic to a torus, by means of which the existence of non-trivial periodic solutions was established. That scheme was then developed and improved for dif­ ferent classes of multidimensional dynamical systems [131, 132, 297, 317, 334, 357, 358]. The method of Poincare mapping [12, 13, 17] in piecewise linear systems was another intensively developed direction.


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