10 research outputs found
Linear Stability of Triangular Equilibrium Points in the Generalized Photogravitational Restricted Three Body Problem with Poynting-Robertson Drag
In this paper we have examined the linear stability of triangular equilibrium
points in the generalised photogravitational restricted three body problem with
Poynting-Robertson drag. We have found the position of triangular equilibrium
points of our problem. The problem is generalised in the sense that smaller
primary is supposed to be an oblate spheroid. The bigger primary is considered
as radiating. The equations of motion are affected by radiation pressure force,
oblateness and P-R drag. All classical results involving photogravitational and
oblateness in restricted three body problem may be verified from this result.
With the help of characteristic equation, we discussed the stability. Finally
we conclude that triangular equilibrium points are unstable.Comment: accepted for publication in Journal of Dynamical Systems & Geometric
Theories Vol. 4, Number 1 (2006
Restricted three body problems at the nanoscale
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