Abstract

The free surface motion in moving containers is an important physical phenomenon for many engineering applications. One way to model the free surface motion is by employing shallow water equations (SWEs). The port-Hamiltonian systems formulation is a powerful tool that can be used for modeling complex systems in a modular way. In this work, we extend previous work on SWEs using the port-Hamiltonian formulation, by considering the two-dimensional equations under rigid body motions. The resulting equations consist of a mixed-port-Hamiltonian system, with finite and infinite-dimensional energy variables and ports. 2000 Math Subject Classification: 34K30, 35K57, 35Q80, 92D25

中文翻译：

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移动容器中二维浅水方程的Port-Hamiltonian模型

摘要

对于许多工程应用而言，移动容器中的自由表面运动是重要的物理现象。一种模拟自由表面运动的方法是采用浅水方程（SWE）。汉密尔顿港系统公式化是一种功能强大的工具，可用于以模块化方式对复杂系统进行建模。在这项工作中，我们通过考虑刚体运动下的二维方程，使用波特-哈密尔顿公式扩展了先前关于超临界水的工作。所得方程由混合端口哈密顿系统组成，具有有限和无限维的能量变量和端口。2000年数学学科分类：34K30、35K57、35Q80、92D25