Asymptotic approximations of first integrals for a nonlinear oscillator (Q1849039)
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scientific article; zbMATH DE number 1836649
| Language | Label | Description | Also known as |
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| English | Asymptotic approximations of first integrals for a nonlinear oscillator |
scientific article; zbMATH DE number 1836649 |
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Asymptotic approximations of first integrals for a nonlinear oscillator (English)
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28 November 2002
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It is shown that the perturbation method based on integrating factors can be used efficiently to approximate first integrals for a generalized Rayleigh oscillator. The method can also be applied to other nonlinear oscillator equations that are integrable when the small parameter is zero. An asymptotic justification of the presented perturbation method is given. For the nonlinear Rayleigh oscillation, it is shown when there exists one stable periodic solution and when there are two periodic solutions.
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integrating factor
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integrating vector
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first integral
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perturbation method
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asymptotic approximation of first integrals
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