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C. Rößler, I. Hafner:
"Index Reduction and Regularisation Methods for Multibody Systems";
in: "Mathmod 2015 Vienna", 44; F. Breitenecker, A. Kugi, I. Troch (ed.); issued by: TU Wien; ARGESIM / ASIM, German Simulation Society, Division of German Society for Informatics and Life Sciences, Wien, 2015, ISBN: 978-3-901608-46-9, 306 - 311.

The use of object-oriented simulation tools for modelling of physical or mechanical systems leads to systems of differential-algebraic equations (DAEs)with a high differential index. The differential index indicates the minimal number of differentiations of the system which are necessary to extract a system of ordinary differential equations from the differentiated system. Especially in mechanics the use of a global coordniate system to describe the different occurring states leads to a DAE that usually has differential index three. In general the numerical solution for ordinary differential equations is very complex. Therefor methods for solving this problem are necessary, which leads to the so-called index reduction. In the following seven methods, where most of them are discussed in detail in Hairer, and Wanner (2002), are considered.

http://dx.doi.org/10.3182/20150218-3-AU-30250

http://publik.tuwien.ac.at/files/PubDat_245367.pdf