## 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.

Author: | Sebastian Reich |
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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 |

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): | Keine 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 |