This project investigates new computational methods for prototyping physical systems with desired dynamical behaviors, with expected applications in design and control engineering. It develops a computational environment for visualizing and manipulating dynamics of physical systems through a combination of numerical and symbolic computations. More specifically, this project studies (1) automated characterization of dynamical systems through analytic and geometric analysis, and (2) techniques for interactive synthesis, optimization, and visualization of dynamics, for example, ``computational scissors'' that cut-and-paste vector fields and shape the desired dynamical properties (e.g. stability regions) for a complex system that is otherwise difficult to design.
