论文标题
浮动3D打印对象的数学
Mathematics of Floating 3D Printed Objects
论文作者
论文摘要
我们通过数学建模和实验探索浮动对象的稳定性。我们的模型基于重心，浮力中心和阿基米德原理的标准思想。我们研究了各种具有二维横截面的浮动形状，并在分析和/或计算上识别有助于识别稳定且不稳定的浮动方向的势能环境。我们将分析和计算与对通过3D打印设计和创建的浮动对象进行了比较。除结果外，我们还提供了测试新形状的浮动配置的代码，并提供了3D打印对象的方法的详细信息。该论文包括猜想和开放问题，以进行进一步研究。
We explore the stability of floating objects through mathematical modeling and experimentation. Our models are based on standard ideas of center of gravity, center of buoyancy, and Archimedes' Principle. We investigate a variety of floating shapes with two-dimensional cross sections and identify analytically and/or computationally a potential energy landscape that helps identify stable and unstable floating orientations. We compare our analyses and computations to experiments on floating objects designed and created through 3D printing. In addition to our results, we provide code for testing the floating configurations for new shapes, as well as giving details of the methods for 3D printing the objects. The paper includes conjectures and open problems for further study.
