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首页> 外文期刊>Planetary and space science >Existence and linear stability of equilibrium points in the Robe's restricted three body problem when the first primary is an oblate spheroid
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Existence and linear stability of equilibrium points in the Robe's restricted three body problem when the first primary is an oblate spheroid

机译：当第一个原初是扁球体时，Robe受限三体问题中平衡点的存在性和线性稳定性

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摘要

The existence and linear stability of equilibrium points in the Robe's restricted three body problem have been studied after considering the full buoyancy force as in Plastino and Plastino and by assuming the hydrostatic equilibrium figure of the first primary as an oblate spheroid. The pertinent equations of motion are derived and existence of all equilibrium points is discussed. It is found that there is an equilibrium point near the centre of the first primary. Further there can be one more equilibrium point on the line joining the centre of the first primary and second primary and infinite number of equilibrium points lying on a circle in the orbital plane of the second primary provided the parameters occurring in the problem satisfy certain conditions. So, there can be infinite number of equilibrium points contrary to the classical restricted three body problem.
机译：在考虑了Plastino和Plastino中的完全浮力并假设第一个主要的静水平衡图为扁球体之后，研究了Robe受限三体问题中平衡点的存在和线性稳定性。推导了相关的运动方程，并讨论了所有平衡点的存在。发现在第一个原边的中心附近有一个平衡点。此外，在连接第一原边和第二原边的中心的线上可以存在一个平衡点，并且只要在问题中出现的参数满足某些条件，第二个原边的轨道平面上的圆上就可以存在无数个平衡点。因此，与经典的受限三体问题相反，可以有无数个平衡点。

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