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

  • Kurt Schlacher
  • Andreas Kugi
  • Kurt Zehetleitner
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2630)


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.


Normal Form Computer Algebra Equivalence Problem Minimal Basis Smooth Section 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Kurt Schlacher
    • 1
    • 2
  • Andreas Kugi
    • 3
  • Kurt Zehetleitner
    • 1
  1. 1.Department of Automatic Control and Control Systems TechnologyJohannes Kepler University of LinzAustria
  2. 2.Christian Doppler Laboratory for Automatic Control of Mechatronic Systems in Steel IndustriesLinzAustria
  3. 3.University of SaarlandGermany

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