Computer algebra methods for implicit dynamic systems and applications

This contribution deals with the application of computer algebra methods to the analysis of systems of implicit ordinary differential equations. These systems are identified with submanifolds in a suitable jet space. We propose an implementation of the accessibility and observability analysis for implicit ordinary differential equations based on Lie group methods. Since this approach requires that the system of equations is formally integrable, we present an algorithm which converts the given system into this form. In addition, it is shown how the efficiency of the stated algorithms can be improved for polynomial systems with the application of Groebner bases. The presented algorithms are applied to the model of the PVTOL aircraft.