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Symbolic Methods for the Equivalence Problem for Systems of Implicit Ordinary Differential Equations

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Symbolic and Numerical Scientific Computation (SNSC 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2630))

Abstract

This contribution deals with the equivalence problem for systems of implicit ordinary differential equations. Equivalence means that every solution of the original set of equations is a solution of a given normal form and vice versa. Since we describe this system as a submanifold in a suitable jet-space, we present some basics from differential and algebraic geometry and give a short introduction to jet-theory and its application to systems of differential equations. The main results of this contribution are two solutions for the equivalence problem, where time derivatives of the input are admitted or not. Apart from the theoretical results we give a sketch for computer algebra based algorithms necessary to solve these problems efficiently.

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References

  1. Boothby, W.J. (1986): An Introduction to Differentiable Manifolds and Riemannian Geometry, Academic Press, Orlando.

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  5. Saunders, D.J. (1989): The Geometry of Jet Bundles, London Mathematical Society Lecture Note Series 142, Cambridge University Press, Cambridge.

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Author information

Authors and Affiliations

  1. Department of Automatic Control and Control Systems Technology, Johannes Kepler University of Linz, Austria

    Kurt Schlacher & Kurt Zehetleitner

  2. Christian Doppler Laboratory for Automatic Control of Mechatronic Systems in Steel Industries, Linz, Austria

    Kurt Schlacher

  3. University of Saarland, Germany

    Andreas Kugi (Chair of System Theory and Automatic Control)

Authors
  1. Kurt Schlacher
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  2. Andreas Kugi
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  3. Kurt Zehetleitner
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Editor information

Editors and Affiliations

  1. RISC-Linz, Johannes Kepler University Linz, Altenberger Str. 69, 4040, Linz, Austria

    Franz Winkler

  2. Institute of Computational Mathematics, Johannes Kepler University Linz, Altenberger Str. 69, 4040, Linz, Austria

    Ulrich Langer

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© 2003 Springer-Verlag Berlin Heidelberg

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Schlacher, K., Kugi, A., Zehetleitner, K. (2003). Symbolic Methods for the Equivalence Problem for Systems of Implicit Ordinary Differential Equations. In: Winkler, F., Langer, U. (eds) Symbolic and Numerical Scientific Computation. SNSC 2001. Lecture Notes in Computer Science, vol 2630. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45084-X_5

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  • DOI: https://doi.org/10.1007/3-540-45084-X_5

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40554-2

  • Online ISBN: 978-3-540-45084-9

  • eBook Packages: Springer Book Archive

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