Mathematical Sciences: Topics in Geometric Mechanics and Symplectic Geometry

数学科学：几何力学和辛几何专题

• 批准号: 8922699
• 负责人: Tudor Ratiu
• 金额: $ 5.64万
• 依托单位: University of California-Santa Cruz
• 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: 1990-06-01 至 1993-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8922699&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Topics; Geometric; Mechanics

The principal investigator will use fiber bundle theory systematically to study Hamiltonian mechanics and symplectic geometry, bifurcation of relative equilibria, linearization of flows along orbits, optimal control of deformable bodies, and the geometry of the group of symplectic diffeomorphisms and of Teichmuller space. Modern symplectic geometry has been used to analyze problems arising from the study of mechanical systems. The principal investigator will use one of the new tools from this geometry known as "fiber bundle theory." In use for the problems at hand, these are bundles of symmetric groups or movements which are mathematically attached to each point of a surface or hypersurface. An elementary example would be a reflection of each plane tangent to a given sphere.

主要研究人员将使用纤维丛理论系统地研究哈密顿力学和辛几何、相对平衡的分叉、沿轨道流动的线性化、变形体的最优控制、辛微分同胚群和TeichMuller空间的几何。现代辛几何已被用来分析机械系统研究中出现的问题。首席研究人员将使用这一几何学中的一种新工具--“纤维束理论”。对于手头的问题，这些是对称群或运动的丛，它们在数学上附加到曲面或超曲面的每个点上。一个基本的例子是与给定球体相切的每个平面的反射。