Perturbed damped pendulum: finding periodic solutions

Abstract

Using the damped pendulum system we introduce the averaging method to study the periodic solutions of a dynamical system with small perturbation. We provide sufficient conditions for the existence of periodic solutions with small amplitude of the non--linear perturbed damped pendulum. The averaging theory provides a useful means to study dynamical systems, accessible to Master and PhD students.

References in corpus (2)

• On the birth of limit cycles for non-smooth dynamical systems
• On the periodic solutions of a perturbed double pendulum

Cited by in corpus (1)

• A Melnikov analysis on a family of second order discontinuous differential equations