{"product_id":"frequency-methods-in-oscillation-theory-von-i-m-burkin-g-a-leonov-a-i-shepeljavyi","title":"Frequency Methods in Oscillation Theory","description":"\u003cp\u003eThe 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.\u003c\/p\u003e\u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9780792338963\"\u003e\u003ch3\u003e\u003c\/h3\u003e\u003c\/div\u003e\u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9789401065702\"\u003e\u003ch3\u003e\u003c\/h3\u003e\u003c\/div\u003e","brand":"Libri","offers":[{"title":"Hardcover - 9780792338963","offer_id":51484884422,"sku":"9780792338963","price":106.99,"currency_code":"EUR","in_stock":true},{"title":"Softcover - 9789401065702","offer_id":39415251501149,"sku":"9789401065702","price":106.99,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0940\/0622\/files\/591b50d8-174d-4cc0-9d18-55576e6c7423.jpg?v=1772176442","url":"https:\/\/shop.autorenwelt.de\/products\/frequency-methods-in-oscillation-theory-von-i-m-burkin-g-a-leonov-a-i-shepeljavyi","provider":"Autorenwelt Shop","version":"1.0","type":"link"}