Dynamical system of relativistic particle under one dimensional harmonic oscillator potential

Abstract

Abstract Dynamical system of a relativistic particle under harmonic oscillator potential was considered through its stability. We first construct the Hamiltonian of the system, which represents the dynamic motion of the relativistic particle. The stability of the system was then determined by the singular point. We found that the relativistic motion under the harmonic oscillator is a stable system where the phase curve forms an ellipse.