Periodic oscillations of the relativistic pendulum with friction

Abstract

We consider the existence and multiplicity of periodic oscillations for the forced pendulum model with relativistic effects by using the Poincare-Miranda theorem. Some detailed information about the bound for the period of forcing term is obtained. To support our analytical work, we also consider a forced pendulum oscillator with the special force $\gamma_0\sin(\omega t)$ including a sufficiently small parameter. The result shows us that for all $\omega\in(0,+\infty)$, there exists a $2\pi/\omega$ periodic solution under our settings.

Keywords

• Relativistic pendulum
• Poincare-Miranda theorem
• averaging
• periodic solutions