Weakly nonlinear oscillations: A perturbative approach
The perturbative analysis of a one-dimensional harmonic oscillator subject to a small nonlinear perturbation is developed within the framework of two popular methods: normal forms and multiple time scales. The systems analyzed are the Duffing oscillator, an energy conserving oscillatory system, the...
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| Veröffentlicht in: | American journal of physics 2004-04, Vol.72 (4), p.538-552 |
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| container_title | American journal of physics |
| container_volume | 72 |
| creator | Kahn, Peter B. Zarmi, Yair |
| description | The perturbative analysis of a one-dimensional harmonic oscillator subject to a small nonlinear perturbation is developed within the framework of two popular methods: normal forms and multiple time scales. The systems analyzed are the Duffing oscillator, an energy conserving oscillatory system, the cubically damped oscillator, a system that exhibits damped oscillations, and the Van der Pol oscillator, which represents limit-cycle systems. Special emphasis is given to the exploitation of the freedom inherent in the calculation of the higher-order terms in the expansion and to the comparison of the application of the two methods to the three systems. |
| doi_str_mv | 10.1119/1.1648687 |
| format | Article |
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| ispartof | American journal of physics, 2004-04, Vol.72 (4), p.538-552 |
| issn | 0002-9505 1943-2909 |
| language | eng |
| recordid | cdi_scitation_primary_10_1119_1_1648687 |
| source | AIP Journals (American Institute of Physics) |
| subjects | Oscillators Physics Science education |
| title | Weakly nonlinear oscillations: A perturbative approach |
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