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. (2012). Closed form integration of a hyperelliptic, odd powers, undamped oscillator. MECCANICA, 47, 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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