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

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.

Published in Nonlinear Dynamics (NODY) journal

References in corpus (3)

• Investigating the nature of motion in 3D perturbed elliptic oscillators displaying exact periodic orbits
• Application of new dynamical spectra of orbits in Hamiltonian systems
• A semi-numerical method for periodic orbits in a bisymmetrical potential

Cited by in corpus (6)

• A Hamiltonian system of three degrees of freedom with eight channels of escape: The Great Escape
• Escapes in Hamiltonian systems with multiple exit channels: Part I
• Dynamical Configurations of Celestial Systems Comprised of Multiple Irregular Bodies
• Revealing the evolution, the stability and the escapes of families of resonant periodic orbits in Hamiltonian systems
• Escapes in Hamiltonian systems with multiple exit channels: Part II
• Exploring the origin, the nature and the dynamical behaviour of distant stars in galaxy models