  This paper discusses model order reduction of large sparse second-order
index-3 differential algebraic equations (DAEs) by applying Iterative Rational
Krylov Algorithm (IRKA). In general, such DAEs arise in constraint mechanics,
multibody dynamics, mechatronics and many other branches of sciences and
technologies. By deecting the algebraic equations the second-order index-3
system can be altered into an equivalent standard second-order system. This can
be done by projecting the system onto the null space of the constraint matrix.
However, creating the projector is computationally expensive and it yields huge
bottleneck during the implementation. This paper shows how to find a reduce
order model without projecting the system onto the null space of the constraint
matrix explicitly. To show the efficiency of the theoretical works we apply
them to several data of second-order index-3 models and experimental resultants
are discussed in the paper.
