Extracting Qualitative Dynamics from Numerical Experiments,
Abstract
One central problem in Qualitative Physics is the qualitative prediction of long-time behavior of physical systems. The machinery developed for qualitative reasoning - qualitative state vector, quantity space, and limit analysis - are largely applicable to systems which are piecewise well approximated by low-order linear systems or by first-order nonlinear differential equations. Typical nonlinear systems - those commonly encountered in Physics - exhibit a far richer spectrum of dynamical behavior. Look at the simplest non trivial form of conservative systems, the area-preserving maps, to provide a new source of examples for investigation into the fundamental issues of descriptive language, style of reasoning, and representation techniques. To automate the experimenting process, two key problems automatic experiment control, and result interpretation, have to be solved. Knowledge of qualitative dynamics and bifurcaitons provides a strong constraint on the type of dynamical behavior possible. This constraint can be exploited to solve the problems. An approach to the control problem is based on this idea. The main result is an implemented program which solves the interpretation problem by using techniques from computational geometry and computer vision.
Document Details
- Document Type
- Technical Report
- Publication Date
- Mar 01, 1987
- Accession Number
- ADA183633
Entities
People
- Kenneth M. Yip
Organizations
- Massachusetts Institute of Technology