A Study in Non-holonomic Dynamics

PI研究非完整动力学中的各种问题。研究内容涉及刚性理论、连续和离散时间完全可积系统理论、接触几何理论和希尔方程理论。研究的主题是连续与离散、刚性与柔性之间的相互作用。研究的方法大多是几何的。该项目是在过去几年里PI在这些领域的工作基础上发展起来的。本研究项目在车辆运动理论、追逐问题、理论机器人和漂浮理论等多个应用领域具有重要影响。发展的方法和新的见解将在当代各种其他感兴趣的问题中找到应用，这些问题由常微分方程和有限差分方程建模。PI是宾夕法尼亚州立大学数学高级研究学期项目（MASS）的主任。该项目通过吸引MASS参与者，来自美国各地的高级本科生，并影响他们在数学和相关学科的职业选择，产生了额外的影响。

The PI studies a variety of problems in non-holonomic dynamics. The study is related with rigidity theory, the theory of completely integrable systems with continuous and discrete time, contact geometry, and the theory of Hill's equation. The main theme of the research is an interaction between continuous and discrete, and between rigidity and flexibility. The methods of study are mostly geometrical. The project has grown out of the PI's work in these areas in the last several years.This research project has a potential of making an impact in a number of applied fields including vehicle motion theory, pursuit problems, theoretical robotics, and flotation theory. The developed methods and new insights will find applications in various other problems of contemporary interest, modeled by ordinary differential and finite difference equations. The PI is the Director of the Mathematics Advance Studies Semesters Program (MASS) at Penn State. The project has an additional impact by engaging the MASS participants, advanced undergraduate students from across the USA, and influencing their career choices in mathematics and related disciplines.