Analytical Solution for the Cubic-Quintic Duffing Oscillator Equation with Physics Applications
The nonlinear differential equation governing the periodic motion of the one-dimensional, undamped, and unforced cubic-quintic Duffing oscillator is solved exactly by obtaining the period and the solution. The period is given in terms of the complete elliptic integral of the first kind and the solut...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2022/9269957 |
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| _version_ | 1849309031545438208 |
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| author | Alvaro H. Salas Lorenzo J. Martínez H David L. Ocampo R |
| author_facet | Alvaro H. Salas Lorenzo J. Martínez H David L. Ocampo R |
| author_sort | Alvaro H. Salas |
| collection | DOAJ |
| description | The nonlinear differential equation governing the periodic motion of the one-dimensional, undamped, and unforced cubic-quintic Duffing oscillator is solved exactly by obtaining the period and the solution. The period is given in terms of the complete elliptic integral of the first kind and the solution involves Jacobian elliptic functions. We solve the cubic-quintic Duffing equation under arbitrary initial conditions. Physical applications are provided. The solution to the mixed parity Duffing oscillator is also formally derived. We illustrate the obtained results with concrete examples. We give high accurate trigonometric approximations to the Jacobian function cn. |
| format | Article |
| id | doaj-art-05ee1ce4fb6e4e6f8dc7582f3aef5f28 |
| institution | Kabale University |
| issn | 1099-0526 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-05ee1ce4fb6e4e6f8dc7582f3aef5f282025-08-20T03:54:16ZengWileyComplexity1099-05262022-01-01202210.1155/2022/9269957Analytical Solution for the Cubic-Quintic Duffing Oscillator Equation with Physics ApplicationsAlvaro H. Salas0Lorenzo J. Martínez H1David L. Ocampo R2Department of Mathematics and StatisticsDepartment of Mathematics and StatisticsDepartment of Mathematics and StatisticsThe nonlinear differential equation governing the periodic motion of the one-dimensional, undamped, and unforced cubic-quintic Duffing oscillator is solved exactly by obtaining the period and the solution. The period is given in terms of the complete elliptic integral of the first kind and the solution involves Jacobian elliptic functions. We solve the cubic-quintic Duffing equation under arbitrary initial conditions. Physical applications are provided. The solution to the mixed parity Duffing oscillator is also formally derived. We illustrate the obtained results with concrete examples. We give high accurate trigonometric approximations to the Jacobian function cn.http://dx.doi.org/10.1155/2022/9269957 |
| spellingShingle | Alvaro H. Salas Lorenzo J. Martínez H David L. Ocampo R Analytical Solution for the Cubic-Quintic Duffing Oscillator Equation with Physics Applications Complexity |
| title | Analytical Solution for the Cubic-Quintic Duffing Oscillator Equation with Physics Applications |
| title_full | Analytical Solution for the Cubic-Quintic Duffing Oscillator Equation with Physics Applications |
| title_fullStr | Analytical Solution for the Cubic-Quintic Duffing Oscillator Equation with Physics Applications |
| title_full_unstemmed | Analytical Solution for the Cubic-Quintic Duffing Oscillator Equation with Physics Applications |
| title_short | Analytical Solution for the Cubic-Quintic Duffing Oscillator Equation with Physics Applications |
| title_sort | analytical solution for the cubic quintic duffing oscillator equation with physics applications |
| url | http://dx.doi.org/10.1155/2022/9269957 |
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