Hamel's Formalism and its Applications

哈梅尔的形式主义及其应用

• 批准号: 1211454
• 负责人: Dmitry Zenkov
• 金额: $ 14万
• 依托单位: North Carolina State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2012
• 资助国家: 美国
• 起止时间: 2012-09-01 至 2017-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1211454&HistoricalAwards=false
• 关键词: Hamel; Formalism; its; Applications

This project develops a representation of Lagrangian mechanics in which the velocity components are measured relative to a frame that is not related to any local coordinates on the configuration space. This approach offers more flexibility than the original formalism of Lagrange, while keeping a clear distinction between system configurations and velocities. Known to be an effective and powerful tool in finite-dimensional continuous-time mechanics, this formalism introduced by Georg Hamel has not yet been fully developed for systems with infinitely-many degrees of freedom. The project is aimed at systematic study of the formalism in the infinite-dimensional setting, understanding its variational structure, its applications to dynamics of infinite-dimensional systems with nonholonomic constraints, including stability of a liquid-filled rigid body subject to nonholonomic constraints, and Lyapunov function construction.Systems with infinite number of degrees of freedom arise in many applications in engineering and industry. Examples include flexible structures and rigid bodies interacting with fluids. This project develops the mathematics required to model and simulate the behavior of such complex mechanical systems. This work on the mechanics of systems will further integrate mathematics and theoretical engineering. The results of the project will be useful in theoretical analysis, simulations, control, and study of the long time behavior of multi-body dynamics and complex mechanical systems.

这个项目开发了拉格朗日力学的表示，其中速度分量是相对于一个框架测量的，该框架与配置空间上的任何局部坐标无关。这种方法提供了更多的灵活性比原来的形式主义的拉格朗日，同时保持一个明确的区别系统的配置和速度。已知是有限维连续时间力学中的有效和强大的工具，由Georg Hamel引入的这种形式主义尚未完全发展为具有无限多自由度的系统。该项目旨在系统地研究无限维环境中的形式主义，了解其变分结构，及其在具有非完整约束的无限维系统动力学中的应用，包括受非完整约束的充液刚体的稳定性，以及李雅普诺夫函数的构造。具有无限自由度的系统在工程和工业中的许多应用中出现。实例包括与流体相互作用的柔性结构和刚性体。该项目开发了建模和模拟此类复杂机械系统行为所需的数学。这项关于系统力学的工作将进一步整合数学和理论工程。 该项目的成果将有助于多体动力学和复杂机械系统的理论分析、仿真、控制和长时间行为的研究。