Abstract
A known one-dimensional, undamped, anharmonic, unforced oscillator whose restoring force is a displacement’s odd polynomial function, is exactly solved via the Gauss and Appell hypergeometric functions, revealing a new fully integrable nonlinear system. Our t=t(x) equation—and its correspondent x=x(t) obtained via the Lagrange reversion approach—can then added to the (not rich) collection of highly nonlinear oscillating systems integrable in closed form. Finally, the hypergeometric formula linking the period T to the initial motion amplitude a is then assumed as a benchmark for ranking the approximate values of the relevant literature.
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Mingari Scarpello, G., Ritelli, D. Closed form integration of a hyperelliptic, odd powers, undamped oscillator. Meccanica 47, 857–862 (2012). https://doi.org/10.1007/s11012-011-9455-8
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DOI: https://doi.org/10.1007/s11012-011-9455-8