Steiner's circumellipse is the unique geometric regularization of any triangle to a circumscribed ellipse with the same centroid, a regularization that motivates our introduction of the Steiner triangle as a minimal model for liquid droplet dynamics. The Steiner drop is a deforming triangle with one side making sliding contact against a planar basal support. The center of mass of the triangle is governed by Newton's law. The resulting dynamical system lives in a four dimensional phase space and exhibits a rich one-parameter family of dynamics. Two invariant manifolds are identified with "bouncing" and "rocking" periodic motions; these intersect at the stable equilibrium and are surrounded by nested quasiperiodic motions. We study the inherently interesting dynamics and also find that this model, however minimal, can capture space-time symmetries of more realistic continuum drop models.

中文翻译：

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斯坦纳三角下落动力学。

Steiner的外接椭圆是任何三角形到具有相同质心的外接椭圆的独特几何正则化，这种正则化促使我们引入Steiner三角形作为液滴动力学的最小模型。Steiner下落器是一个变形三角形，其一侧与平面的基础支撑滑动接触。三角形的质心受牛顿定律支配。最终的动力学系统生活在一个四维相空间中，并展现出丰富的动力学一参数系列。用“弹跳”和“摇摆”周期运动来识别两个不变的歧管。它们在稳定平衡处相交，并被嵌套的拟周期运动所包围。我们研究了内在有趣的动力学，并且发现该模型无论多么小，