[Zurück]

C. Rößler, I. Hafner:
"Index Reduction and Regularisation Methods for Multibody Systems";
IFAC PapersOnLine, 48 (2015), 1; S. 306 - 311.

Abstract: This paper presents regularisation methods for differential-algebraic equations of mechanical systems. These systems can be described via systems of differential and algebraic equations that usually have differential index three. Such systems are typically gained by the use of multibody simulation tools, where the system is composed of connected rigid and flexible bodies and different joints and the underlying equations are derived automatically by the
software. The considered methods in this paper are applicable to differential-algebraic equations of index three and are divided into three basic approaches: index reduction with differentiation,
stabilisation by projection and methods based on state space transformation. The methods using differentiation are the substitution of the constraint equations by derivatives, the Baumgarte-Method and the Pantelides-Algorithm with the use of Dummy Derivatives. Furthermore two methods using projection are considered: the orthogonal projection method and the symmetric projection method. The next approach uses a local coordinate transformation to reduce the index. Lastly the Gear-Gupta-Leimkuhler formulation is considered. At the end the advantages and disadvantages of all these methods are discussed and a basic outline on the functionality and the requirements for the implementation of each method is given.

DAE, Differential Index, Index Reduction, Mechanical Systems, Regularisation

http://dx.doi.org/10.1016/j.ifacol.2015.05.150

http://publik.tuwien.ac.at/files/publik_253627.pdf