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 G.; Ritelli D.. - In: MECCANICA. - ISSN 0025-6455. - STAMPA. - 47:(2012), pp. 857-862. [10.1007/s11012-011-9455-8]
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.File in questo prodotto:
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