Ritelli, Daniele ; Mingari Scarpello, Giovanni
(2012)
Closed form integration of a hyperelliptic oscillator.
Meccanica, 47
(4).
pp. 857-862.
ISSN 0025-6455
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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.
Abstract