  In this paper, we investigate some of the classical restricted three body
problems at the nanoscale, such as the circular planar restricted problem for
three C60 fullerenes, and a carbon atom and two C60 fullerenes. We model the
van der Waals forces between the fullerenes by the Lennard-Jones potential. In
particular, the pairwise potential energies between the carbon atoms on the
fullerenes are approximated by the continuous approach, so that the total
molecular energy between two fullerenes can be determined analytically. Since
we assume that such interactions between the molecules occur at sufficiently
large distance, the classical three body problems analysis is legitimate to
determine the collective angular velocity of the two and three C60 fullerenes
at the nanoscale. We find that the maximum angular frequency of the two and
three fullerenes systems reach the terahertz range and we determine the
stationary points and the points which have maximum velocity for the carbon
atom for the carbon atom and the two fullerenes system.
