Approximate Potentials with Applications to Strongly Nonlinear Oscillators with Slowly Varying Parameters

A method of approximate potential is presented for the study of certain kinds of strongly nonlinear oscillators. This method is to express the potential for an oscillatory system by a polynomial of degree four such that the leading approximation may be derived in terms of elliptic functions. The adv...

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Main Authors:	Jianping Cai, Y.P. Li
Format:	Article
Language:	English
Published:	Hindawi Limited 2003-01-01
Series:	Shock and Vibration
Online Access:	http://dx.doi.org/10.1155/2003/364790

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spelling	doaj-238aa1f5751e43b28406291ee119d81c2020-11-24T23:58:08ZengHindawi LimitedShock and Vibration1070-96221875-92032003-01-01105-637938610.1155/2003/364790Approximate Potentials with Applications to Strongly Nonlinear Oscillators with Slowly Varying ParametersJianping Cai0Y.P. Li1Department of Mathematics, Zhangzhou Teachers College, Fujian 363000, ChinaDepartment of Mathematics, Zhongshan University, Guangzhou 510275, ChinaA method of approximate potential is presented for the study of certain kinds of strongly nonlinear oscillators. This method is to express the potential for an oscillatory system by a polynomial of degree four such that the leading approximation may be derived in terms of elliptic functions. The advantage of present method is that it is valid for relatively large oscillations. As an application, the elapsed time of periodic motion of a strongly nonlinear oscillator with slowly varying parameters is studied in detail. Comparisons are made with other methods to assess the accuracy of the present method.http://dx.doi.org/10.1155/2003/364790
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Jianping Cai Y.P. Li
spellingShingle	Jianping Cai Y.P. Li Approximate Potentials with Applications to Strongly Nonlinear Oscillators with Slowly Varying Parameters Shock and Vibration
author_facet	Jianping Cai Y.P. Li
author_sort	Jianping Cai
title	Approximate Potentials with Applications to Strongly Nonlinear Oscillators with Slowly Varying Parameters
title_short	Approximate Potentials with Applications to Strongly Nonlinear Oscillators with Slowly Varying Parameters
title_full	Approximate Potentials with Applications to Strongly Nonlinear Oscillators with Slowly Varying Parameters
title_fullStr	Approximate Potentials with Applications to Strongly Nonlinear Oscillators with Slowly Varying Parameters
title_full_unstemmed	Approximate Potentials with Applications to Strongly Nonlinear Oscillators with Slowly Varying Parameters
title_sort	approximate potentials with applications to strongly nonlinear oscillators with slowly varying parameters
publisher	Hindawi Limited
series	Shock and Vibration
issn	1070-9622 1875-9203
publishDate	2003-01-01
description	A method of approximate potential is presented for the study of certain kinds of strongly nonlinear oscillators. This method is to express the potential for an oscillatory system by a polynomial of degree four such that the leading approximation may be derived in terms of elliptic functions. The advantage of present method is that it is valid for relatively large oscillations. As an application, the elapsed time of periodic motion of a strongly nonlinear oscillator with slowly varying parameters is studied in detail. Comparisons are made with other methods to assess the accuracy of the present method.
url	http://dx.doi.org/10.1155/2003/364790
work_keys_str_mv	AT jianpingcai approximatepotentialswithapplicationstostronglynonlinearoscillatorswithslowlyvaryingparameters AT ypli approximatepotentialswithapplicationstostronglynonlinearoscillatorswithslowlyvaryingparameters
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Approximate Potentials with Applications to Strongly Nonlinear Oscillators with Slowly Varying Parameters

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