肥皂膜悬链的现场观测--一个简单的教育物理实验
In-situ observation of a soap film catenoid - a simple educational physics experiment
摘要：
欧拉-拉格朗日方程的解是一个极值泛函，为了理解泛函在局部极值（最大值或最小值）处是平稳的，我们提出了一个物理实验，涉及使用肥皂膜形成悬链。悬链面是两个同轴圆环之间形成的曲面，在数学上被归类为最小曲面。我们使用肥皂膜在两个圆环之间创建悬链面，并在改变圆环之间距离的情况下原位表征悬链面。肥皂膜的形状非常有趣，可以用动态力学来解释。通过观察悬链线，物理学生可以观察到局部极值现象。我们强调，现场观察肥皂膜悬链是一个适当的物理实验，结合理论和实验。
英文摘要：
The solution to the Euler-Lagrange equation is an extremal functional.To understand that the functional is stationary at local extrema (maxima or minima), we propose a physics experiment that involves using soap film to form a catenoid. A catenoid is a surface that is formed between two coaxial circular rings and is classified mathematically as a minimal surface.Using soap film, we create catenoids between two rings and characterize the catenoid in-situ while varying distance between rings. The shape of the soap film is very interesting and can be explained using dynamic mechanics. By observing catenoid, physics students can observe local extrema phenomena. We stress that in-situ observation of soap film catenoids is an appropriate physics experiment that combines theory and experimentation.
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