Mathematical Sciences: Qualitative Analysis of Dynamical Systems

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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.