Perturbed damped pendulum: finding periodic solutions

TL;DR

This paper applies the averaging method to analyze the existence of small-amplitude periodic solutions in a perturbed damped pendulum system, offering accessible insights into nonlinear dynamical systems for students.

Contribution

It introduces the averaging method to find periodic solutions in a perturbed damped pendulum, providing new sufficient conditions for their existence.

Findings

Sufficient conditions for periodic solutions are established.

The averaging method effectively analyzes nonlinear perturbed systems.

Results are accessible to students at Master and PhD levels.

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.