A global solution curve for a class of periodic problems, including the relativistic pendulum

TL;DR

This paper investigates the global structure of periodic solutions in a class of forced equations, including the relativistic pendulum, using continuation methods and numerical bifurcation diagrams.

Contribution

It generalizes the analysis of the relativistic pendulum to a broader class of equations and provides a numerical approach for studying solution bifurcations.

Findings

Existence of multiple periodic solutions

Numerical bifurcation diagrams illustrating solution structure

Applicability of continuation methods to these problems

Abstract

Using continuation methods, we study the global solution structure of periodic solutions for a class of periodically forced equations, generalizing the case of relativistic pendulum. We obtain results on the existence and multiplicity of periodic solutions. Our approach is suitable for numerical computations, and in fact we present some numerically computed bifurcation diagrams illustrating our results.