Stability of equilibrium points in a CR3BP with oblate bodies enclosed by a circular cluster of material points |
| |
| Authors: | Jagadish Singh Joel John Taura |
| |
| Institution: | 1. Department of Mathematics, Faculty of Science, Ahmadu Bello University, Zaria, Nigeria
2. Department of Mathematics and Computer Science, Faculty of Science, Federal University, Kashere, Nigeria
|
| |
| Abstract: | We have investigated an improved version of the classic restricted three-body problem where both primaries are considered oblate and are enclosed by a homogeneous circular planar cluster of material points centered at the mass center of the system. In this dynamical model we have examined the effect on the number and on the linear stability of the equilibrium locations of the small particle due to both, the primaries’ oblateness and the potential created by the circular cluster. We have drawn the zero-velocity surfaces and we have found that in addition to the usual five Lagrangian equilibrium points of the classic restricted three-body problem, there exist two new collinear points L n1,L n2 due to the potential from the circular cluster of material points. Numerical investigations reveal that with the increase in the mass of the circular cluster of material points, L n2 comes nearer to the more massive primary, while L n1 moves away from it. Owing to oblateness of the bodies, L n1 comes nearer to the more massive primary, while L n2 moves towards the less massive primary. The collinear equilibrium points remain unstable, while the triangular points are stable for 0<μ<μ c and unstable for $\mu_{c} \le \mu \le \frac{1}{2}$ , where μ c is the critical mass ratio influenced by oblateness of the primaries and the potential from the circular cluster of material points. The oblateness and the circular cluster of material points have destabilizing tendency. |
| |
| Keywords: | |
| 本文献已被 SpringerLink 等数据库收录！ |
|
