Energy Growth, Dissipation, and Control in Hamiltonian Systems

哈密​​顿系统中的能量增长、耗散和控制

• 批准号: 2307718
• 负责人: Marian Gidea
• 金额: $ 30万
• 依托单位: Yeshiva University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2023
• 资助国家: 美国
• 起止时间: 2023-07-15 至 2026-06-30
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2307718&HistoricalAwards=false
• 关键词: Energy; Growth; Dissipation; Control; Hamiltonian

This project will enhance the foundational understanding of Dynamical Systems through the development of theories, models, and techniques that could potentially address a range of contemporary scientific and technological issues, such as production of sustainable energy and space exploration. The main objective of this research is to devise mechanisms to gain energy in mechanical systems subject to dissipation and forcing. The project will study mathematical models for energy harvesting devices, which convert external vibrations into electrical energy, and will optimize their energy output. It will also investigate the dynamics of comets, asteroids, and spacecraft, with applications to the design of fuel-efficient space missions. Partial support will be provided to graduate and undergraduate students, including members of underrepresented groups. The project will open new research directions in the study of Hamiltonian systems subject to general perturbations. It will advance the understanding of the Arnold diffusion phenomenon, describing that integrable Hamiltonian systems subject to small, generic, Hamiltonian perturbations, exhibit orbits along which the energy changes by a significant amount. The project will investigate this phenomenon in concrete systems, such as from celestial mechanics. It will also explore the case of perturbations given by conformally symplectic vector fields, which model the effect of dissipation. Additionally, the project will develop novel methods to use natural perturbations of a system as controllers, in order to drive the system from some given state to any desired state.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

该项目将通过发展理论，模型和技术来增强对动态系统的基本理解，这些理论，模型和技术有可能解决一系列当代科学和技术问题，例如生产可持续能源和太空探索。这项研究的主要目的是设计机制，以获取受耗散和强迫的机械系统中的能量。该项目将研究能源收集设备的数学模型，这些模型将外部振动转化为电能，并将优化其能量输出。它还将研究彗星，小行星和航天器的动力学，并应用于燃油效率空间任务的设计。将为研究生和本科生提供部分支持，包括代表性不足的小组的成员。该项目将在对哈密顿系统的研究中开放新的研究方向，但受到一般扰动的影响。它将提高对Arnold扩散现象的理解，描述可容纳小型，通用的，哈密顿的扰动的综合性汉密尔顿系统，表现出轨道，能量会大量变化。该项目将在混凝土系统中研究这种现象，例如来自天体力学。它还将探讨通过共核矢量场给出的扰动情况，该场对耗散的效果进行了建模。 此外，该项目将开发新的方法来使用系统的自然扰动作为控制器，以将系统从某些状态推动到任何所需的状态。该奖项反映了NSF的法定任务，并被认为是值得通过基金会的知识分子优点和更广泛影响的审查标准通过评估来获得支持的。