Singh Jagadish, Tyokyaa Richard K
Department of Mathematics, Faculty of Physical Sciences, Ahmadu Bello University, Zaria, Nigeria.
Department of Mathematical Sciences, Faculty of Physical Sciences, Federal University Dutsin-Ma, Katsina, Nigeria.
Heliyon. 2023 Feb 13;9(3):e13708. doi: 10.1016/j.heliyon.2023.e13708. eCollection 2023 Mar.
The study investigates the collinear positions and stability in the elliptic restricted synchronous three-body problem under an oblate primary and a dipole secondary for Luhman 16 and HD188753 systems. Our study has established four collinear equilibrium points which are greatly affected by the parameters under review. The collinear position move away and closer as the parameters increase and decrease respectively. For the collinear positions , we witnessed a uniform space movement away from the origin in the negative direction while seems to be moving closer to the origin from the negative part of the origin. We observed changes in the movements of the collinear positions as a result of the half distance between the mass dipoles and the oblateness of the primary for the problem under review. The movements away and closer to the origin from collinear positions do not change the status of the collinear points as they remain unstable and unchanged. It is also found that as the half distance between mass dipoles and oblateness of the primary increase, the region of stability of the collinear positions decreases for the aforementioned binary systems. The collinear equilibrium point is stable for the characteristic roots for system. This is evidenced by at least one characteristic root, a positive real part and a complex root. The stability of collinear points in most cases are unstable for the stated binary systems in Lyapunov.
该研究调查了在扁率主星和偶极子次星情况下，卢曼16和HD188753系统椭圆限制同步三体问题中的共线位置和稳定性。我们的研究建立了四个共线平衡点，它们受到所研究参数的极大影响。随着参数分别增加和减少，共线位置会远离和靠近。对于共线位置 ，我们看到其在负方向上有远离原点的均匀空间运动，而 似乎从原点的负半轴部分向原点靠近。由于所研究问题中质量偶极子之间的半距离和主星的扁率，我们观察到共线位置的运动发生了变化。从共线位置远离和靠近原点的运动不会改变共线点的状态，因为它们仍然不稳定且不变。还发现，随着质量偶极子之间的半距离和主星扁率的增加，上述双星系统中共线位置的稳定区域减小。对于 系统，共线平衡点 对于特征根 是稳定的。这由至少一个具有正实部的特征根和一个复根证明。在李雅普诺夫意义下，对于所述双星系统，大多数情况下共线点的稳定性是不稳定的。
