Perturbed damped pendulum: finding periodic solutions via averaging method

Agraïments: The author is supported by a FAPESP-BRAZlL grant 2012/10231-7Using the damped pendulum model we introduce the averaging method to study the periodic solutions of dynamical systems with small non-autonomous perturbation. We provide sufficient conditions for the existence of periodic solutions with small amplitude of the non-linear perturbed damped pendulum. The averaging method provides a useful means to study dynamical systems, accessible to Master and PhD students