Are semi-numerical methods an effective tool for locating periodic orbits in 3D potentials?

TL;DR

This paper evaluates a semi-numerical approach for efficiently locating and calculating the periods of 3D periodic orbits in a composite potential, showing high agreement with numerical integration results.

Contribution

It demonstrates that semi-numerical methods are effective and reliable for finding periodic orbits in complex 3D potentials with harmonic and perturbative components.

Findings

Semi-numerical results closely match numerical integration outcomes.

Semi-numerical methods offer a fast alternative for orbit detection.

Comparison shows semi-numerical methods are reliable in various resonant cases.

Abstract

A semi-numerical method is used in order to locate the position and calculate the period of periodic orbits in a 3D composite bisymmetrical potential, in a number of resonant cases. The potential consists of a 3D harmonic oscillator and a Plummer sphere. The outcomes are compared with results found using the numerical integration of the equations of motion and the agreement is very good. This agreement strongly suggests, that semi-numerical methods can be used in order to obtain fast and reliable results regarding the position and period of the periodic orbits in 3D composite potentials with a harmonic oscillator part and different kinds of perturbations. Comparison with other methods of obtaining 3D periodic orbits is discussed.