Summary
The most important characteristics of the non-local oscillator, an oscillator subjected to an additional non-local force, are extensively studied by means of a new asymptotic perturbation method that is able to furnish an approximate solution of weakly non-linear differential equations. The resulting motion is doubly periodic, because a second little frequency appears, in addition to the fundamental harmonic frequency. Comparison with the numerical solution obtained by the Runge-Kutta method confirms the validity of the asymptotic perturbation method and its importance for the study of non-linear dynamical systems.
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Maccari, A. The non-local oscillator. Nuov Cim B 111, 917–930 (1996). https://doi.org/10.1007/BF02743288
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DOI: https://doi.org/10.1007/BF02743288