Abstract In the present work, we shall show an exhaustive numerical analysis of the dynamical behavior of the test particle in the modified restricted three-body problem with variable mass in which the extra effect of the three-body interaction is also taken into account. This additional force ingredient appears in the potential of the classical problem as a new extra term. As the main results, we determine the motion for test particle, under the effect of three-body interaction, which varies its mass according to Jeans’ law (Jeans (1928)). The number and existence of the libration points along with their stability have been investigated as the function of value of the parameters which occur due to variable mass of the test particle. Moreover, the regions of the possible motion are also unveiled where the test particle is free to move. Furthermore, the multivariate version of the Newton-Raphson (NR) iterative scheme is used to determine the outcomes of the used parameters on the topology of the basins of convergence (BoC) linked to the libration points. The numerical analysis shows that the topology of the basins of convergence linked with the libration points are highly influenced by the used parameters. Moreover, we perform a systematic analysis to unveil how the regions of convergence are related with the number of required iterations and also with the corresponding probability distributions.

中文翻译：

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改进的变质量圆形受限三体问题

摘要 在目前的工作中，我们将对测试粒子在变质量受限三体问题中的动力学行为进行详尽的数值分析，其中还考虑了三体相互作用的额外影响。这个额外的力成分作为一个新的额外项出现在经典问题的潜力中。作为主要结果，我们确定了测试粒子在三体相互作用的影响下的运动，其质量根据 Jeans 定律（Jeans (1928)）发生变化。已经研究了振动点的数量和存在以及它们的稳定性作为由于测试粒子的可变质量而出现的参数值的函数。此外，还揭示了测试粒子可以自由移动的可能运动区域。此外，Newton-Raphson (NR) 迭代方案的多元版本用于确定所用参数对连接到振动点的收敛盆地 (BoC) 拓扑结构的结果。数值分析表明，与振动点相连的辐合盆地的拓扑结构受所用参数的影响很大。此外，我们进行了系统分析，以揭示收敛区域与所需迭代次数以及相应的概率分布之间的关系。数值分析表明，与振动点相连的辐合盆地的拓扑结构受所用参数的影响很大。此外，我们进行了系统分析，以揭示收敛区域与所需迭代次数以及相应的概率分布之间的关系。数值分析表明，与振动点相连的辐合盆地的拓扑结构受所用参数的影响很大。此外，我们进行了系统分析，以揭示收敛区域与所需迭代次数以及相应的概率分布之间的关系。