CONICET | Buscador de Institutos y Recursos Humanos

Techniques are developed to find all periodic solutions in the simple pendulumby means of the homotopy analysis method (HAM). This involves thesolution of the equations of motion in two different coordinate representations.Expressions are obtained for the cycles and periods of oscillations with ahigh degree of accuracy in the whole range of amplitudes. Moreover, theconvergence of the method is easily checked. The aim of this work is toshow how the dynamic of a simple example of oscillatory systems may bestudied globally with the HAM and to incentivate the interest of advancedundergraduate students in this type of techniques.