{"product_id":"frequency-methods-in-oscillation-theory-g-a-leonov-9780792338963","title":"Frequency Methods in Oscillation Theory","description":"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.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eAuthor:\u003c\/b\u003e G. a. Leonov,I. M. Burkin,A. I. Shepeljavyi\u003cbr\u003e\u003cb\u003eISBN-10:\u003c\/b\u003e 0792338960\u003cbr\u003e\u003cb\u003eISBN-13:\u003c\/b\u003e 9780792338963\u003cbr\u003e\u003cb\u003ePublisher:\u003c\/b\u003e Springer\u003cbr\u003e\u003cb\u003eLanguage:\u003c\/b\u003e English\u003cbr\u003e\u003cb\u003ePublished:\u003c\/b\u003e 12\/31\/1995\u003cbr\u003e\u003cb\u003ePages:\u003c\/b\u003e 404\u003cbr\u003e\u003cb\u003eFormat:\u003c\/b\u003e Hardcover\u003cbr\u003e\u003cb\u003eWeight:\u003c\/b\u003e 1.68lbs\u003cbr\u003e\u003cb\u003eSize:\u003c\/b\u003e 9.21h x 6.14w x 0.94d","brand":"G. a. Leonov","offers":[{"title":"Hardcover","offer_id":48457720103167,"sku":"9780792338963","price":109.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0662\/2982\/9887\/files\/img_722bc6ac-12ed-4f24-abe2-02aac47c4b11.jpg?v=1777400645","url":"https:\/\/www.whiterainbookhouse.com\/products\/frequency-methods-in-oscillation-theory-g-a-leonov-9780792338963","provider":"WR Book House","version":"1.0","type":"link"}