A GEOMETRIC TREATMENT OF IMPLICIT DIFFERENTIAL-ALGEBRAIC EQUATIONS

A differential-geometric approach for proving the existence and unique ness of implicit differential-algebraic equations is presented. It pro vides for a significant improvement of an earlier theory developed by the authors as well as for a completely intrinsic definition of the in dex of such problems. The differential-algebraic equation is transform ed into an explicit ordinary differential equation by a reduction proc ess that can be abstractly defined for specific submanifolds of tangen t bundles here called reducible pi-submanifolds. Local existence and u niqueness results for differential-algebraic equations then follow dir ectly from the final stage of this reduction by means of an applicatio n of the standard theory of ordinary differential equations. (C) 1994 Academic Press, Inc.