On a geometrical interpretation of differential-algebraic equations

  • The subject of this paper is the relation of differential-algebraic equations (DAEs) to vector fields on manifolds. For that reason, we introduce the notion of a regular DAE as a DAE to which a vector field uniquely corresponds. Furthermore, a technique is described which yields a family of manifolds for a given DAE. This socalled family of constraint manifolds allows in turn the formulation of sufficient conditions for the regularity of a DAE. and the definition of the index of a regular DAE. We also state a method for the reduction of higher-index DAEs to lowsr-index ones that can be solved without introducing additional constants of integration. Finally, the notion of realizability of a given vector field by a regular DAE is introduced, and it is shown that any vector field can be realized by a regular DAE. Throughout this paper the problem of path-tracing is discussed as an illustration of the mathematical phenomena.

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Metadaten
Author:Sebastian Reich
URN:urn:nbn:de:kobv:517-opus-46683
Series (Serial Number):Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe (paper 157)
Document Type:Postprint
Language:English
Date of Publication (online):2010/09/13
Year of Completion:1990
Publishing Institution:Universität Potsdam
Release Date:2010/09/13
Source:Circuits, Systems, and Signal Processing 9 (1990), 4, S. 367-382
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
Licence (German):License LogoKeine Nutzungslizenz vergeben - es gilt das deutsche Urheberrecht
Notes extern:
first published in:
Circuits, Systems, and Signal Processing 9 (1990), 4, p. 367-382
doi: 10.1007/BF01189332