毛细浮动和台球问题
Capillary floating and the billiard ball problem
摘要：
我们建立了毛细管之间的连接浮动在中性平衡和台球问题。这使我们能够减少问题的浮动在中性平衡在任何方向与规定的接触角无限均匀的圆柱体的问题有关台球焦散线的正交横截面。我们解决了台球问题。作为一个应用程序，我们描述了可能的接触角，并展示了一个无限的家庭真正的分析非圆形的圆柱体，浮动在中性平衡，在任何方向与恒定的接触角。
英文摘要：
We establish a connection between capillary floating in neutral equilibrium and the billiard ball problem. This allows us to reduce the question of floating in neutral equilibrium at any orientation with a prescribed contact angle for infinite homogeneous cylinders to a question about billiard caustics for their orthogonal cross-sections. We solve the billiard problem. As an application, we characterize the possible contact angles and exhibit an infinite family of real analytic non-round cylinders that float in neutral equilibrium at any orientation with constant contact angles.
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