In this paper, we investigate some restricted three body problems such as circular planar
restricted problems for three C60 fullerenes and a carbon atom and two C60 fullerenes.
We model the residual van der Waals forces between 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 molecules occur at sufficiently large distance, the classical three body
problem analysis is legitimate to determine the collective angular velocities 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 terahertz range and discover the stationary
points and points with maximum velocity of the carbon atom for the carbon atom and
two fullerenes system.