scholarly journals Motion in the Restricted Three-Body Problem at the Nanoscale

Author(s):  
Jagadish Singh ◽  
Tyokyaa K. Richard

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.

2020 ◽  
Vol 4 (2) ◽  
pp. 523-531
Author(s):  
K. R. Tyokyaa ◽  
Tersoo Atsue

This paper investigates the positions and stability of libration points in the framework of the circular restricted three-body problem for the systems: Luyten726-8 and HD98800. The position of the third body lie in the plane almost directly above and below the center of the oblate primary. It is found that radiations and oblateness of the primary have destabilizing effects; the presence of any one or more of the latter makes weak the stabilizing ability of the former, consequently the overall effect is that the range of stability of the libration points decreases. Considering the range of stability and instability, that is  and , the libration points are respectively stable and unstable for HD98800 and Luyten 762-8 systems. Our results show that, all the roots are real, and for each set of values, there exist at least a positive real part and hence in the Lyapunov sense, the stability of the libration points are unstable for the systems HD98800 and Luyten 762-8.


New Astronomy ◽  
2021 ◽  
Vol 84 ◽  
pp. 101510
Author(s):  
Md Sanam Suraj ◽  
Rajiv Aggarwal ◽  
Md Chand Asique ◽  
Amit Mittal

2007 ◽  
Vol 17 (04) ◽  
pp. 1151-1169 ◽  
Author(s):  
MARIAN GIDEA ◽  
JOSEP J. MASDEMONT

The stable and unstable invariant manifolds associated with Lyapunov orbits about the libration point L1between the primaries in the planar circular restricted three-body problem with equal masses are considered. The behavior of the intersections of these invariant manifolds for values of the energy between that of L1and the other collinear libration points L2, L3is studied using symbolic dynamics. Homoclinic orbits are classified according to the number of turns about the primaries.


Sign in / Sign up

Export Citation Format

Share Document