受限制三體問題在雙星運動(dynamics of binary)、聚星(multiple stars)以及行星系統(planetary system)中是眾所皆知且非常重要的。所以，我們在此篇文章研究一個受限制三體問題，此受測質點除了受雙黑洞一般的萬有引力影響外，還包含了星系的萬有引力位能。最後我們發現，除了找到一般的五個平衡點外(有三個平衡點在x軸上，另外兩個平衡點皆在平行y軸的線上)，在不同的情況及條件下，存在新的平衡點在此系統上。

The restricted three-body problem is well-known and very important for dynamics of binary, multiple stars and also planetary systems. So, motivated by Jiang \& Yeh (2006), we study the motion of a test particle influenced by the gravitational force from the central binary black holes and the galaxy.
In addition to the usual five equilibrium points (three collinear and two triangular points),
there are some new equilibrium points for this problem.
We studied the conditions for the existence of these new equilibrium points analytically.

Jiang, I.-G., Yeh, L.-C., On the Chermnykh-Like Problems: I The Mass Parameter u=0.5, Astrophysics and Space Science (2006) VOL 305, pp 341-348

Jiang, I.-G., Yeh, L.-C., On the Chermnykh-Like Problems: II The Equilibrium Points, (2006) VOL, 306 pp 189-200

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