Mathematical Sciences: Analysis and Control of Mechanical and Dynamical Systems

这个项目的目的是分析一些有实际意义的数学系统的动力学和控制。首先，我们将使用最近发展起来的能量动量方法来研究旋转系统的动力学和控制。提出了一种用能量-Casimir方法镇定不稳定控制系统的新方法。有限维降维和从稳定到不稳定的过渡将被研究。最后，首席研究人员将尝试将他最近在Toda晶格上的工作扩展到对某些梯度和哈密顿系统的进一步理解。

The object of this project is to analyze the dynamics and control of a number of mathematical systems of practical interest. In the first place the dynamics and control of rotating systems will be studied using recently developed Energy- Momentum methods. A new approach to stabilizing unstable control systems by the Energy-Casimir method will be considered. Finite dimensional reductions and transit from stability to unstability will be studied. Finally, the principal investigator will try to extend his recent work on Toda lattice to further understanding of certain gradient and Hamiltonian systems.