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
Exact solution to a first-fifth power nonlinear unforced oscillator / Mingari Scarpello G.; Ritelli D.. - In: APPLIED MATHEMATICAL SCIENCES. - ISSN 1312-885X. - STAMPA. - 4:(2010), pp. 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 literatureI documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
