Mathematical Sciences: The Dynamics of Digital Computers andMechanical Systems

数学科学：数字计算机和机械系统的动力学

• 批准号: 8703429
• 负责人: Richard McGehee
• 金额: $ 12.07万
• 依托单位: University of Minnesota-Twin Cities
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1987
• 资助国家: 美国
• 起止时间: 1987-07-01 至 1990-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8703429&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Dynamics; Digital; Computers

Richard McGehee proposes to carry out research on two topics. These involve the application of the theory of dynamical systems to digital circuits and a study of the dynamical systems on finite state spaces which arise from approximations of continuous systems. Richard Moeckel's work will be concerned with an investigation of collisions and of rejection to infinity in the three body problem, a study of central configurations in the n-body problem, and an investigation of normal forms near elliptic fixed points of mechanical systems. The research on finite approximation of continuous dynamical systems recognises the fact that computer experiments can necessarily only reveal approximations of the original continuous system. The focus of attention will be on questions asking whether the properties of attractors of the original system are faithfully exhibited on the video screen. McGehee's other project is to study the mathematical idealizations of the digital and analog levels of hardware and develop a theory of how digital devices can be derived from analog circuits. Moeckel's work will continue studies of periodic points and invariant curves of area preserving maps, of homoclinic phenomena and of normal forms. These investigations are all aimed towards an understanding of the possible qualitative behaviors of three point masses. The study of central configurations is important in the context of escape to infinity, multiple collisions, and the topology of energy surfaces.

理查德·麦基希建议对两个 话题这些都涉及到动力学理论的应用 系统到数字电路和动力系统的研究 在有限状态空间中， 连续系统。理查德·莫克尔的作品将关注 对碰撞和排斥到无穷大的研究， 三体问题，一个中心构型的研究， n-体问题，以及对近似正规形的研究 力学系统的椭圆不动点 连续动力系统有限逼近的研究 系统认识到计算机实验可以 必然只揭示原始连续的近似， 系统注意力的焦点将集中在问题上， 原系统吸引子的性质是否 忠实地展现在屏幕上。麦基希的另一个项目 是研究数字的数学理想化， 模拟水平的硬件，并制定了一个理论， 器件可以从模拟电路得到。 Moeckel的工作将继续研究周期点， 同宿现象的保面积映射的不变曲线 的正常形式。这些调查都是针对 了解三种可能的定性行为， 质点中心构型的研究对于 逃逸到无穷大，多重碰撞， 能量曲面的拓扑结构。