NDLI: Theoretical Aspects of Nonlinear Oscillations

Content Provider	IEEE Xplore Digital Library
Author	Minorsky, N.
Copyright Year	1953
Description	This review gives an outline of the modern theory of nonlinear oscillations. This field, originated about four decades ago by the late Prof. B. van der Pol, acquired a considerable momentum in recent years with a gradually increasing number of ramifications, some of which are still in a state of development. For this reason the selection of topics for this review is narrowed down to matters which have reached a state of a reasonable codification. It has been assumed that a certain amount of familiarity with these topics is available on the part of the reader so that only essential points are emphasized. Topological methods and analytical methods are written in a condensed manner, while special attention is given to the stroboscopic method, which is probably less known, and which is used extensively later. A survey of the principal nonlinear phenomena investigated under the assumption of near linearity is given. Phenomena of parametric excitation, subharmonic resonance and synchronization are outlined with some detail, but those of the so called asynchronous actions are treated less completely as their detailed presentation would lengthen the paper unduly. The final section of this review deals with the so called "piece-wise linear phenomena;" it transcends already purely analytic methods and belongs to recent developments concerning nonlinear and nonanalytic oscillations often encountered in the theory of automatic regulation and control.
Starting Page	368
Ending Page	381
Page Count	14
File Size	1832696
File Format	PDF
ISSN	00962007
Volume Number	7
Issue Number	4
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	1960-12-01
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Automatic control Econometrics Systems biology Astronomy Differential equations Electric shock Nonlinear equations Resonance
Content Type	Text
Resource Type	Article
Subject	Electrical and Electronic Engineering

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