A new approach to nonlinear quartic oscillators

被引:0
|
作者
Rami Ahmad El-Nabulsi
Waranont Anukool
机构
[1] Chiang Mai University,Research Center for Quantum Technology, Faculty of Science
[2] Chiang Mai University,Department of Physics and Materials Science, Faculty of Science
[3] Athens Institute for Education and Research,Mathematics and Physics Divisions
来源
Archive of Applied Mechanics | 2022年 / 92卷
关键词
Nonstandard Lagrangians; Quadratic damping; Jacobi elliptic functions; 37J05; 70F40; 34C15;
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摘要
In this study, we proved that damped quadratic nonlinear oscillators similar to Duffing and Helmholtz–Duffing damped equations which emerge in bubble dynamics with time-periodic straining flows and solitary-like wave's dynamics may be derived from a new functional approach based on nonstandard Lagrangians and fractional frictions. The solutions of these equations are given in terms of the Jacobi elliptic functions. It was observed that the dynamical model constructed in this study is comparable to dynamical systems with natural Lagrangians for which the Riemann structure is conformally flat which has important implications in dynamical systems with position-dependent mass.
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页码:351 / 362
页数:11
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