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力系统的基础理解，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，例如可持续能源的生产和太空探索。这项研究的主要目标是设计在受到耗散和强迫的机械系统中获取能量的机制。该项目将研究能量收集装置的数学模型，这些装置将外部振动转化为电能，并优化其能量输出。它还将研究彗星、小行星和航天器的动力学，并将其应用于节能太空任务的设计。将为研究生和本科生提供部分支持，包括代表性不足群体的成员。该项目将为研究受一般扰动影响的哈密顿系统开辟新的研究方向。它将增进对阿诺德扩散现象的理解，描述可积哈密顿系统受到小的、通用的哈密顿扰动，表现出能量沿着其轨道发生显着变化。该项目将研究具体系统中的这种现象，例如天体力学。它还将探讨共形辛矢量场给出的扰动情况，该矢量场对耗散效应进行建模。 此外，该项目将开发新颖的方法来使用系统的自然扰动作为控制器，以便将系统从某个给定状态驱动到任何期望的状态。该奖项反映了 NSF 的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准。