The nonlinear pendulum: formulas for the large amplitude period

P. Amore, M. Cervantes Valdovinos, G. Ornelas, S. Zamudio Barajas


A simple and precise formula for the period of a nonlinear pendulum is obtained using the Linear Delta Expansion, a powerful non--perturbative technique which has been applied in the past to problems in different areas of physics. Our result is based on a systematic approach which allows us to obtain a new series for the elliptic integrals, in terms of which the exact solution of our problem is cast. A further improvement of the LDE result is then obtained by using Padé approximants. Finally we make a comparison with other approximations in the literature for the period of the pendulum, valid either at small or at large angles.


Perturbation theory; linear delta expansion; pendulum

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Revista Mexicana de Física E

ISSN: 2683-2216 (on line), 1870-3542 (print)

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