In this paper we discuss the time integration of multibody system model equations
following a novel approach that has originally been developed for the time integration of linear
differential-algebraic equations of arbitrary high index. We do not restrict ourselves to classical
constrained mechanical systems but consider the more complex model equations that are actually
used in state-of-the-art multibody system simulation packages. The equations of motion form a
system of differential-algebraic equations of differentiation index 3 with a special structure that we
will exploit in the numerical solution. We replace the equations of motion by a so-called projected
differentiation index-one differential-algebraic equation with the same solution set.
In this paper we present the new numerical algorithm GEOMS for the numerical integration of the most general form of the equations of motion of multibody systems, including nonholonomic constraints and possible redundancies in the constraints, as they may appear in industrial applications. Besides the numerical integration it offers some additional features like stabilization of the model equations, use of different decomposition strategies, or checking and correction of the initial values with respect to their consistency. Furthermore, GEOMS preserves hidden constraints and (possibly) existing solution invariants if they are provided as equations.
We will also demonstrate the performance and the applicability of GEOMS for two mechanical examples of different degrees of complexity.