Mass variation effect in CR3B problem with nanoscale

Abstract

The aim of this paper is to investigate the dynamical behavior of a Carbon atom under the forces of the two fullerenes in the circular restricted three-body (CR3B) configuration with nanoscale. Here, we assume that the mass of a Carbon atom varies according to the Jeans law, and then with the use of Meshcherskii transformation, we determine the equations of motion and quasi-Jacobian integral. Then by the use of numerical values of the parameters, we investigate the potential surfaces, equilibrium points, regions of motion, Poincaré surfaces of sections, periodic orbits, basins of attraction and stability of the equilibrium points.