Mathematical Sciences: Geometry and Dynamics of Mechanical Systems with Symmetry

小行星9633161 拟议的研究在于几何力学领域。它与奠定经典力学各个方面的理论基础有关。具有对称性的非完整系统是拉格朗日约化思想的一个应用。可积系统和孤子将追求与控制动力学中的某些应用的观点。哈密顿系统中的分歧将在奇异约化的背景下进行研究。还将研究控制系统的几何学。 几何力学的目标是在严格的数学环境中阐述经典力学中的理论和问题。几何力学最近有几项成就。在落猫的例子中，猫在没有施加任何角动量的情况下执行了完全的重新定向，现在已经使用连接的概念进行了解释-连接是一个数学概念，最初是为了研究微分几何中所谓的主丛而引入的。拟议的研究将进一步追求这些理论思想，并考虑在控制理论和机器人等领域的可能应用。

9633161 Marsden The proposed research lies in the area of geometric mechanics. It has to do with laying a theoretical foundation for various aspects of classical mechanics. Nonholonomic systems with symmetry are to be investigated as an application of the ideas of Lagrangian reduction. Integrable systems and solitons will be pursued with a view towards certain applications in control dynamics. Bifurcations in Hamiltonian systems will be investigated in the context of singular reduction. Geometry of control systems will also be studied. Geometric mechanics aims to formulate theories and problems in classical mechanics in a mathematically rigorous setting. There have been several recent successes of geometric mechanics. The falling cat example, where the cat executes a complete re-orientation without exerting any angular momentum, has now been explained using the idea of a connection - a connection is a mathematical notion originally introduced to study so called principal bundles in differential geometry. The proposed research will further pursue these theoretical ideas as well as consider possible applications in such areas as control theory and robotics.