Motion in the Restricted Three-Body Problem at the Nanoscale

Abstract

This paper studies the classical restricted three-body problem of a carbon atom in the vicinity of two carbon 60 fullerenes (  fullerenes) at the nanoscale. The total molecular energy between the two fullerenes is determined analytically by approximating the pairwise potential energies between the carbon atoms on the fullerenes by a continuous approach. Using software MATHEMATICA, we compute the positions of the stationary points and their stability for a carbon atom at the nanosacle and it is observed that for each set of values, there exists at least one complex root with the positive real part and hence in the Lyapunov sense, the stationary points are unstable. Since only attractive Van der Waals forces contribute to the orbiting behavior, no orbiting phenomenon can be observed for , where the Van der Waals forces becomes repulsive. Although the  orbital is speculative in nature and also presents exciting possibilities, there are still many practical challenges that would need to be overcome before the  orbital might be realized. However, the present theoretical study is a necessary precursor to any of such developments.