Abstract

The elliptic case of restricted four-body problem with variable mass of infinitesimal body is studied here. The three primary bodies which are placed at the vertices of an equilateral triangle and moving in the elliptical orbits around their common center of mass. Out of these primaries we have considered that one massive body is having radiating effect and other two bodies are oblate in shapes. The fourth body which have infinitesimal mass, are varying its mass according to Jeans law. We derive the equations of motion of the infinitesimal body under the generalized sense in the elliptic restricted four-body problem by using the Meshcherskii-space time transformations. Further we numerically study about the equilibrium points, Poincaré surfaces of section, regions of possible motion and basins of the attracting domain by considering the variation of parameters used. Further more we examine the stability of these equilibrium points and found them unstable.

中文翻译：

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变质量广义椭圆约束四体问题

摘要

在此研究了具有无限小物体质量的受限四体问题的椭圆情形。三个基体位于等边三角形的顶点，并在椭圆轨道上绕其共同的质心移动。在这些原基中，我们认为一个大的物体正在辐射，而另外两个物体的形状是扁圆形。具有无限小质量的第四物体根据让斯定律变化其质量。利用Meshcherskii-时空变换，推导了椭圆约束四体问题中广义意义下无穷小体的运动方程。此外，我们对截面的平衡点，庞加莱曲面进行了数值研究，通过考虑所用参数的变化，确定可能运动的区域和吸引域的盆地。此外，我们检查了这些平衡点的稳定性，发现它们不稳定。