This work deals with the nonlinear stability of the elliptical restricted three-body problem with oblate and radiating primaries and the oblate infinitesimal. The stability has been analyzed for the resonance cases around and and also the nonresonance cases. It was observed that the motion of the infinitesimal in this system shows instable behavior when considered in the third order resonance. However, for the fourth order resonance the stability is shown for some mass parameters. The motion in the case of nonresonance was found to be unstable. The problem has been numerically applied to study the movement of the infinitesimal around two binary systems, Luyten-726 and Sirius.

中文翻译：

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受椭圆形和辐射原形影响的椭圆约束三体问题中椭圆形无穷小的非线性稳定性

这项工作解决了椭圆约束三体问题的非线性稳定性，该问题具有扁形和辐射原色以及扁形无穷小。分析了周围共振情况的稳定性 和 还有非共振案件 观察到，当在三阶共振中考虑时，该系统中无穷小的运动表现出不稳定的行为。但是，对于四阶共振，显示了某些质量参数的稳定性。发现非共振情况下的运动不稳定。该问题已在数值上应用于研究极小值在两个二元系统Luyten-726和Sirius周围的运动。