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Frequency Methods in Oscillation Theory (Paperback, Softcover reprint of the original 1st ed. 1996)
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Frequency Methods in Oscillation Theory (Paperback, Softcover reprint of the original 1st ed. 1996)
Series: Mathematics and Its Applications, 357
Expected to ship within 18 - 22 working days
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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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