Differential-Geometric Techniques for Solving Differential Algebraic Equations.

摘要

Differential-algebraic systems of equations (DAEs) arise in many areas of science and engineering. In particular, the equations of motion for a constrained mechanical systems considered in this volume are usually modelled as a second order DAE. In recent years the literature on the numerical solution of such systems has grown rapidly. However, up to now, existence theories for nonlinear DAEs are available only for a few selected classes of systems. The differential-geometric approach is based on the observation that, as long as we expect the solution of a DAE to be some smooth path in the space of dependent variables, the system must define a dynamical system in suitable subsets of that space. (KR)