Mathematical Sciences: Qualitative Analysis of Dynamical Systems

8901574 米勒 米勒博士将继续他的定性研究 动力系统的性质。 这样的系统可以被 数学上用微分方程、积分 方程、偏微分方程或它们的组合 这些类型的方程。 他将研究 复杂桁架结构的近似解 其包含粘弹性阻尼元件，所述粘弹性阻尼元件用于 稳定结构并抑制不必要的振动。 他 将研究翻滚粘弹性流体的控制和稳定 零重力结构与双臂柔性机械臂 在一个重力下 他还将研究一种可移动的机械手 问题. 将使用的方法包括函数 分析技术，数值方法，李雅普诺夫理论和 积分方程技术 本研究的结果将提供新的方法， 机械系统振动抑制研究。 它们还将提供分析稳定性的新方法 柔性机械反馈控制系统的性质 系统.

8901574 Miller Dr. Miller will continue his investigations of qualitative properties of dynamical systems. Such systems can be mathematically represented by differential equations, integral equations, partial differential equations or a combination of these types of equations. He will study methods for approximating the solution of complex truss type structures which contain viscoelastic damping elements that are used to stablize the structure and to suppress unwanted vibrations. He will study control and stabilization of a tumbling viscoelastic structure under zero gravity and a two arm flexible manipulator under one gravity. He will also study a movable manipulator problem. The methods which will be used include functional analysis techniques, numerical methods, Lyapunov theory and integral equations techniques. The results of this research will provide new methods of investigation for vibration suppression in mechanical systems. They will also provide new methods of analyzing stability properties of feedback control systems for flexible mechanical systems.