Symbolic Methods for the Equivalence Problem for Systems of Implicit Ordinary Differential Equations
- 395 Downloads
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.
KeywordsNormal Form Computer Algebra Equivalence Problem Minimal Basis Smooth Section
Unable to display preview. Download preview PDF.
- 6.Schlacher, K., Kugi, A. (2001): Control of Nonlinear Descriptor Systems, A Computer Algebra Based Approach, Lecture Notes in Control and Information Sciences, 259, 397–395, Springer, London.Google Scholar