A known one-dimensional, undamped, anharmonic oscillator whose restoring force is an odd polynomial function of displacement, is solved exactly via the Gauss and Appell hypergeometric functions, revealing a new fully integrable nonlinear system. The closed form relationship linking the period T to the initial motion amplitude a can then play as a benchmark to all the approximate values of literature.

Closed form integration of a hyperelliptic, odd powers, undamped oscillator

MINGARI SCARPELLO, GIOVANNI;RITELLI, DANIELE
2012

Abstract

A known one-dimensional, undamped, anharmonic oscillator whose restoring force is an odd polynomial function of displacement, is solved exactly via the Gauss and Appell hypergeometric functions, revealing a new fully integrable nonlinear system. The closed form relationship linking the period T to the initial motion amplitude a can then play as a benchmark to all the approximate values of literature.
Mingari Scarpello G.; Ritelli D.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/117291
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