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The Transient Behavior of Nonlinear Systems

Clauser, Francis H. (1960) The Transient Behavior of Nonlinear Systems. IRE Transactions on Circuit Theory, 7 (4). pp. 446-458. ISSN 0096-2007. http://resolver.caltech.edu/CaltechAUTHORS:20120925-153051814

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Abstract

It is shown that the classical perturbation procedure for treating nonlinear systems leads to solutions expressed as Fourier-like series with slowly varying coefficients. These slowly varying coefficients contain the information about the long term behavior of the system. Inconsistently, the classical perturbation procedure expresses these coefficients as power series, a mode of expression which has notoriously poor long term validity. An operational procedure is presented for treating oscillations having slowly variable amplitudes and frequencies. An extension of the usual impedance concepts is presented for expressing the frequency characteristics of both linear and nonlinear elements when oscillations with many frequencies are present simultaneously and when these oscillations vary in both frequency and amplitude. From these methods, a perturbation procedure is devised which permits the behavior of systems to be computed with any order of accuracy, using only the algebraic processes which are characteristic of operational procedures. This procedure avoids expressing its results in terms of the local time. Instead, it expresses them in terms of the fundamental characteristics of the oscillations which axe present. As a consequence, the final solutions have the much desired long term validity and they may be used to obtain asymptotic estimates of the behavior of the system. The method is able to treat systems containing nonlinear perturbing elements and elements which we have described as moderately nonlinear. By means of examples it is shown that it is a straightforward process to treat systems to second order accuracy. This level of accuracy covers a large number of the intercoupling effects that characterize the more sophisticated nonlinear phenomena.


Item Type:Article
Related URLs:
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http://dx.doi.org/10.1109/TCT.1960.1086711DOIUNSPECIFIED
http://ieeexplore.ieee.org/xpl/articleDetails.jsp?tp=&arnumber=1086711&contentType=Journals+%26+Magazines&sortType%3Dasc_p_Sequence%26filter%3DAND%28p_IS_Number%3A23617%29PublisherUNSPECIFIED
Additional Information:© 1960 IRE. Received by the PGCT, May 16, 1960. Date of Current Version: 06 January 2003. This research was supported by the United States Air Force through the Air Force Office of Scientific Res. of the Air Res. and Dev. Command, under Contract Number AF 49(638)-496. The Johns Hopkins University, Baltimore, Md.
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Air Force Office of Scientific Research (AFOSR)AF 49(638)-496
Record Number:CaltechAUTHORS:20120925-153051814
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20120925-153051814
Official Citation:Clauser, F.; , "The Transient Behavior of Nonlinear Systems," Circuit Theory, IRE Transactions on , vol.7, no.4, pp. 446- 458, Dec 1960 doi: 10.1109/TCT.1960.1086711 URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1086711&isnumber=23617
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:34370
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:25 Sep 2012 22:54
Last Modified:27 Dec 2012 02:43

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