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Fourier series expansion for nonlinear Hamiltonian oscillators
Méndez López, Vicenç (Universitat Autònoma de Barcelona. Departament de Física)
Sans, Cristina (Universitat Autònoma de Barcelona. Grup de Física Estadística)
Campos, Daniel (Universitat Autònoma de Barcelona. Departament de Física)
Llopis, Isaac (Universitat Autònoma de Barcelona. Grup de Física Estadística)

Data: 2010
Resum: The problem of nonlinear Hamiltonian oscillators is one of the classical questions in physics. When an analytic solution is not possible, one can resort to obtaining a numerical solution or using perturbation theory around the linear problem. We apply the Fourier series expansion to find approximate solutions to the oscillator position as a function of time as well as the period-amplitude relationship. We compare our results with other recent approaches such as variational methods or heuristic approximations, in particular the Ren-He’s method. Based on its application to the Duffing oscillator, the nonlinear pendulum and the eardrum equation, it is shown that the Fourier series expansion method is the most accurate.
Drets: Tots els drets reservats.
Llengua: Anglès.
Document: article ; recerca ; publishedVersion
Publicat a: Physical review. E : statistical, nonlinear, and soft matter physics, Vol. 81, Number 6 (June 2010) , p. 066201/1-066201/8, ISSN 1539-3755

DOI: 10.1103/PhysRevE.81.066201

8 p, 315.9 KB

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