凸曲线上点电荷的平衡
Equilibria of point charges on convex curves
摘要：
研究了库仑势影响下凸曲线上三点的平衡位置。我们确定这些位置为orthotripods，曲线上的三个点具有并发法线。这将平衡位置与曲线的焦散线（渐屈线）联系起来。并发法线只能在焦散的核心中相遇，该核心包含在焦散的内部。此外，我们还给出了三点平衡时只带正电荷的几何条件。对于椭圆，我们证明了正交三足类空间同胚于一个二维有界圆柱。
英文摘要：
We study the equilibrium positions of three points on a convex curve under influence of the Coulomb potential. We identify these positions as orthotripods, three points on the curve having concurrent normals. This relates the equilibrium positions to the caustic (evolute) of the curve. The concurrent normals can only meet in the core of the caustic, which is contained in the interior of the caustic. Moreover, we give a geometric condition for three points in equilibrium with positive charges only. For the ellipse we show that the space of orthotripods is homeomorphic to a 2-dimensional bounded cylinder.
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