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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| Format: | Article |
| Language: | English |
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Wiley
2003-01-01
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| Series: | Shock and Vibration |
| Online Access: | http://dx.doi.org/10.1155/2003/364790 |
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| _version_ | 1832563966700683264 |
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| author | Jianping Cai Y.P. Li |
| author_facet | Jianping Cai Y.P. Li |
| author_sort | Jianping Cai |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-238aa1f5751e43b28406291ee119d81c |
| institution | Kabale University |
| issn | 1070-9622 1875-9203 |
| language | English |
| publishDate | 2003-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Shock and Vibration |
| spelling | doaj-art-238aa1f5751e43b28406291ee119d81c2025-02-03T01:12:01ZengWileyShock 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 |
| spellingShingle | Jianping Cai Y.P. Li Approximate Potentials with Applications to Strongly Nonlinear Oscillators with Slowly Varying Parameters Shock and Vibration |
| title | 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_short | 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 |
| url | http://dx.doi.org/10.1155/2003/364790 |
| work_keys_str_mv | AT jianpingcai approximatepotentialswithapplicationstostronglynonlinearoscillatorswithslowlyvaryingparameters AT ypli approximatepotentialswithapplicationstostronglynonlinearoscillatorswithslowlyvaryingparameters |