Abstract

The object-oriented model description of physical or mechanical systems leads to differential-algebraic equations. In general the numerical solution of such equation systems is very complex, numerically extensive or may even be impossible. Therefore it is important to find methods for solving given equation system, this leads to the so-called index reduction and regularization methods. This paper gives a short over-view of common methods of index reduction. Additionally a classification of these different approaches is made. Afterwards each approach is presented in detail and the advantages and disadvantages of the different methods are discussed. In order to compare the different index reduction methods, the methods described above are demonstrated by various examples. For the comparabil-ity of the different methods the obtained numerical solutions and the deviation from the constraint equa-tions are displayed graphically. Therefore the distinct approaches can be compared with regard to their nu-merical solutions. The two examples are mechanical systems with differential index three. The equations of motion of a pendulum on a circular path in Cartesian coordinates and the motion of the double pendulum in Cartesian coordinates, which shows a chaotic behaviour, are used as case studies.