The paper examines instability of triangular equilibrium points of a test particle in the gravitational field of two primaries radiating with effective Poynting–Robertson (P–R) drag, enclosed by circumbinary disc. The equations of motion are derived and positions of triangular equilibrium points are located. It is seen that the locations are affected by the disc, radiation pressure and P–R drag of the primaries. In particular, for our numerical computations of the locations of the triangular equilibrium points and the linear stability analysis, we consider a low-mass pulsating star, IRAS 11472-0800 as the bigger primary, with a young white dwarf star; G29-38 as the smaller primary. We observe that the disc does not change the x-coordinates of the triangular points while their y-coordinates are been altered. However, radiation pressure, P–R drag and the mass parameter µ mainly contribute in shifting the location of the triangular points. As regards the stability analysis, these points are in general unstable under the combine effects of radiation, P–R drag and disc, in the entire range of the mass parameter due to complex roots with positive real parts. Further, in order to discern the effects of the parameters on the instability outcome, we broaden the range of the mass parameter to accommodate small values of the mass parameters. We observe that in the absence of radiation and the presence of disc, when the mass parameter is less than the critical mass, all the roots are pure imaginary and the triangular point is stable. However, when \(\mu = 0.038521\), the four roots are complex, but turn pure imaginary quantities when the disc is present. This proves that the disc is a stabilizing force while the radiation pressure and P–R drag induces instability around the triangular equilibrium points in the entire range of the mass parameter due to the presence of complex roots with positive real parts.

该论文研究了测试粒子在两个主要辐射的引力场中的三角形平衡点的不稳定性，这些初级粒子以有效的坡印廷-罗伯逊 (P-R) 阻力辐射，由外周双星盘包围。推导出运动方程并确定三角平衡点的位置。可以看出，位置受原色盘、辐射压力和 P-R 阻力的影响。特别是，对于三角平衡点位置的数值计算和线性稳定性分析，我们将一颗低质量脉动星 IRAS 11472-0800 视为较大的主星，并带有一颗年轻的白矮星；G29-38 作为较小的初级。我们观察到圆盘不会改变三角形点的x坐标，而它们的y-坐标已更改。然而，辐射压力、P-R 阻力和质量参数μ主要有助于移动三角形点的位置。关于稳定性分析，由于复根具有正实部，这些点在辐射、P-R 阻力和圆盘的综合作用下，在整个质量参数范围内通常是不稳定的。此外，为了辨别参数对不稳定性结果的影响，我们扩大了质量参数的范围以适应质量参数的小值。我们观察到，在没有辐射和圆盘存在的情况下，当质量参数小于临界质量时，所有根都是纯虚的，三角点是稳定的。然而，当\(\mu = 0.038521\)，四个根是复数，但当圆盘存在时变成纯虚数。这证明了圆盘是一个稳定力，而辐射压力和 P-R 阻力在整个质量参数范围内由于存在具有正实部的复根而导致三角形平衡点周围的不稳定性。