A semi-numerical method for periodic orbits in a bisymmetrical potential

TL;DR

This paper introduces a semi-numerical approach to accurately determine the position and period of periodic orbits in a bisymmetrical potential combining harmonic oscillator and Plummer potential, validated against numerical integration.

Contribution

The paper presents a novel semi-numerical method for finding periodic orbits in complex bisymmetrical potentials, demonstrating its reliability and efficiency.

Findings

Semi-numerical results closely match numerical integration outcomes.

Method is effective across multiple resonant cases.

Comparison shows advantages over existing orbit-finding techniques.

Abstract

We use a semi-numerical method to find the position and period of periodic orbits in a bisymmetrical potential, made up of a two dimensional harmonic oscillator, with an additional term of a Plummer potential, in a number of resonant cases. The results are compared with the outcomes obtained by the numerical integration of the equations of motion and the agreement is good. This indicates that the semi-numerical method gives general and reliable results. Comparison with other methods of locating periodic orbits is also made.