Trajectories of two identical particles on a plane in a constant magnetic field subject to non-Coulomb potentials

TL;DR

This paper analyzes the classical trajectories of two identical particles under non-Coulomb potentials in a magnetic field, identifying conditions for bounded and periodic orbits through analytical and numerical methods.

Contribution

It provides necessary and sufficient conditions for bounded and periodic orbits of two particles in a magnetic field with non-Coulomb potentials, combining analytical and numerical approaches.

Findings

Conditions for bounded orbits derived

Periodic orbits characterized

Numerical solutions illustrating theoretical results

Abstract

Study of the classical motion of two identical particles on a plane subject to non-Coulomb potentials in a constant magnetic field presented in polar coordinates. With the rigorous analysis of the potentials and the constants of motion, we are able to give necessary and sufficient conditions for the existence of bounded and periodic orbits. We also show and analyze numerical solutions of Newton equations of motion.