On forced oscillations of a constrained relativistic particle

TL;DR

This paper investigates the conditions under which a relativistic particle constrained on a curve exhibits periodic oscillations, using a geometrical approach, with applications demonstrated through examples like the relativistic pendulum.

Contribution

It provides new sufficient conditions for periodic oscillations of constrained relativistic particles, expanding understanding beyond classical models.

Findings

Derived sufficient conditions for periodic oscillations

Applied results to examples including the relativistic pendulum

Illustrated the geometrical approach for analyzing forced relativistic systems

Abstract

We consider the forced motion of a relativistic particle constrained on a curve and present sufficient conditions for periodic oscillations by means of an illustrative geometrical approach. Obtained result is illustrated by a few examples including the forced relativistic pendulum.