Mathematical Sciences: Reduction Theory in Mechanics and Classical Relativistic Fields

数学科学：力学和经典相对论场中的还原论

• 批准号: 8922704
• 负责人: Jerrold Marsden
• 金额: $ 15.33万
• 依托单位: University of California-Berkeley
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-05-15 至 1993-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8922704&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Reduction; Theory; Mechanics

Reduction of mechanical systems with symmetry will be pursued. The problems to be studied were motivated by recent advances in stability theory and the theory of classical relativistic fields. The block diagonalization technique to be used is based on a recent solution to the problem of separation of rotational and internal modes. The general geometric theory underlying this technique will be investigated. Recent advances in classical field theory based on reduction ideas will be exploited to develop corresponding covariant reduction theory and related topics. This project will extend our understanding of the stability of relativistic magnetic, electrical, and gravitational fields. These fields, which may describe motion, are said to be stable if under various sorts of perturbations the system maintains its basic nature in some way. These have come under intense mathematical scrutiny for several decades and this project will extend our knowledge of them.

将追求减少具有对称性的机械系统。 要研究的问题是由稳定性理论和经典相对论场理论的最新进展推动的。 所使用的块对角化技术基于最近对旋转模式和内部模式分离问题的解决方案。 将研究该技术背后的一般几何理论。 基于约简思想的经典场论的最新进展将被用来发展相应的协变约简理论和相关主题。 该项目将扩展我们对相对论磁场、电场和引力场稳定性的理解。 如果系统在各种扰动下以某种方式保持其基本性质，则可以描述运动的这些场是稳定的。 几十年来，这些问题一直受到严格的数学审查，这个项目将扩展我们对它们的了解。