Controllability for swimming phenomena

游泳现象的可控性

• 批准号: 0504093
• 负责人: Alexander Khapalov
• 金额: --
• 依托单位: Washington State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2005
• 资助国家: 美国
• 起止时间: 2005-07-15 至 2009-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0504093&HistoricalAwards=false
• 关键词: Controllability; swimming; phenomena

The goal of this project is to develop a methodology for the study of controllability properties of complex coupled nonlinear systems of partial and ordinary differential (or integro-differential) equations modeling the swimming phenomena. These systems include the fluid equations (for example, Stokes or Navier-Stokes equations) and the equations describing the position of a swimming device (or a living organism) in the fluid. The swimming motion of the latter is the result of the action of "internal" forces generated by the device, which also serve as the "external" forces for the surrounding fluid. In a typical swimming model the aforementioned internal forces are either the forces, preserving the structure of the device at hand or the "propulsion" forces (for example, of rotation or rowing nature), which make it swim. The magnitudes of the latter forces are modeled as coefficients and serve as nontraditional (in the framework of the mathematical controllability theory) multiplicative or bilinear controls.In this project we will investigate the mathematical nature of the swimming motion of a mechanical device (such as a robotic fish or a robotic eel) or a living organism in a fluid. What makes the latter to swim the way it does? Or more precisely, what kind forces are necessary to employ to achieve the desirable swimming motion? How can we design a mechanical device that can do the same? Answers to these questions are of great interest in biological and medical applications and in engineering applications dealing with propulsion systems in fluids.

该项目的目标是开发一种方法来研究模拟游泳现象的偏微分和常微分（或积分微分）方程的复杂耦合非线性系统的可控性特性。这些系统包括流体方程（例如斯托克斯或纳维-斯托克斯方程）和描述游泳装置（或活体）在流体中的位置的方程。后者的游动是装置产生的“内部”力作用的结果，该“内部”力也充当周围流体的“外部”力。在典型的游泳模型中，上述内力要么是保持手边装置结构的力，要么是使其游泳的“推进”力（例如，旋转或划船性质）。后者的力的大小被建模为系数，并用作非传统（在数学可控性理论的框架中）乘法或双线性控制。在这个项目中，我们将研究机械设备（例如机器鱼或机器鳗）或流体中活生物体游泳运动的数学性质。是什么让后者以这种方式游泳？或者更准确地说，需要使用什么样的力才能实现理想的游泳动作？我们怎样才能设计出具有同样功能的机械装置呢？这些问题的答案对于生物和医学应用以及涉及流体推进系统的工程应用非常有意义。