Dynamics of the helmholtz oscillator with fractional order damping
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| Format: | Artículo científico |
| Sprache: | en |
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Universidad de Guanajuato
2013
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| _version_ | 1876434876576563200 |
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| author | Adolfo Ortiz |
| author_facet | Adolfo Ortiz |
| contents | Dynamics of the helmholtz oscillator with fractional order damping Adolfo Ortiz Jesús M. Seoane J. H. Yan Miguel A. F. Sanjuán Multidisciplinarias (Ciencias Sociales) Grünwald Fractional damping Helmholtz oscillator Letnikov fractional derivative The dynamics of the nonlinear Helmholtz Oscillator with fractional order damping are stud - ied in detail. The discretization of differential equations according to the Grünwald-Letnikov fractional derivative definition in order to get numerical simulations is reported. Comparison between solutions obtained through a fourth-order Runge-Kutta method and the fractional damping system are comparable when the fractional derivative of the damping term a is fixed at 1. That proves the good performance of the numerical scheme. The effect of taking the frac - tional derivative on the system dynamics is investigated using phase diagrams varying a from 0.5 to 1.75 with zero initial conditions. Periodic motions of the system are obtained at certain ranges of the damping term. On the other hand, escape of the trajectories from a potential well result at a certain critical value of the fractional derivative. The history of the displacement as a function of time is shown also for every a selected. 2013 artículo científico 0188-6266 https://www.redalyc.org/articulo.oa?id=41629563003 en http://www.redalyc.org/revista.oa?id=416 Acta Universitaria application/pdf Universidad de Guanajuato Acta Universitaria (México) Num.2 Vol.23 |
| format | Artículo científico |
| id | redalyc_41629563003 |
| institution | Redalyc |
| language | en |
| publishDate | 2013 |
| publisher | Universidad de Guanajuato |
| spellingShingle | Dynamics of the helmholtz oscillator with fractional order damping Adolfo Ortiz Multidisciplinarias (Ciencias Sociales) Grünwald Fractional damping Helmholtz oscillator Letnikov fractional derivative Dynamics of the helmholtz oscillator with fractional order damping Adolfo Ortiz Jesús M. Seoane J. H. Yan Miguel A. F. Sanjuán Multidisciplinarias (Ciencias Sociales) Grünwald Fractional damping Helmholtz oscillator Letnikov fractional derivative The dynamics of the nonlinear Helmholtz Oscillator with fractional order damping are stud - ied in detail. The discretization of differential equations according to the Grünwald-Letnikov fractional derivative definition in order to get numerical simulations is reported. Comparison between solutions obtained through a fourth-order Runge-Kutta method and the fractional damping system are comparable when the fractional derivative of the damping term a is fixed at 1. That proves the good performance of the numerical scheme. The effect of taking the frac - tional derivative on the system dynamics is investigated using phase diagrams varying a from 0.5 to 1.75 with zero initial conditions. Periodic motions of the system are obtained at certain ranges of the damping term. On the other hand, escape of the trajectories from a potential well result at a certain critical value of the fractional derivative. The history of the displacement as a function of time is shown also for every a selected. 2013 artículo científico 0188-6266 https://www.redalyc.org/articulo.oa?id=41629563003 en http://www.redalyc.org/revista.oa?id=416 Acta Universitaria application/pdf Universidad de Guanajuato Acta Universitaria (México) Num.2 Vol.23 |
| title | Dynamics of the helmholtz oscillator with fractional order damping |
| topic | Multidisciplinarias (Ciencias Sociales) Grünwald Fractional damping Helmholtz oscillator Letnikov fractional derivative |
| url | https://www.redalyc.org/articulo.oa?id=41629563003 |