A one-dimensional, undamped, anharmonic oscillator whose restoring force is an odd polynomial function of displacement, is solved exactly through the elliptic functions and inverted, providing oscillation amplitude through time, and then revealing a new fully integrable nonlinear system. The closed form relationship linking the period $mathbb{T}$ to the initial motion amplitude textit{a} can then play as a benchmark to the approximate values of literature
Mingari Scarpello G., Ritelli D. (2010). Exact solution to a first-fifth power nonlinear unforced oscillator. APPLIED MATHEMATICAL SCIENCES, 4, 3589-3594.
Exact solution to a first-fifth power nonlinear unforced oscillator
MINGARI SCARPELLO, GIOVANNI;RITELLI, DANIELE
2010
Abstract
A one-dimensional, undamped, anharmonic oscillator whose restoring force is an odd polynomial function of displacement, is solved exactly through the elliptic functions and inverted, providing oscillation amplitude through time, and then revealing a new fully integrable nonlinear system. The closed form relationship linking the period $mathbb{T}$ to the initial motion amplitude textit{a} can then play as a benchmark to the approximate values of literatureFile in questo prodotto:
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