  Recently various numerical integration schemes have been proposed for
numerically simulating the dynamics of constrained multibody systems (MBS)
operating. These integration schemes operate directly on the MBS configuration
space considered as a Lie group. For discrete spatial mechanical systems there
are two Lie group that can be used as configuration space: $SE\left( 3\right) $
and $SO\left( 3\right) \times \mathbb{R}^{3}$. Since the performance of the
numerical integration scheme clearly depends on the underlying configuration
space it is important to analyze the effect of using either variant. For
constrained MBS a crucial aspect is the constraint satisfaction. In this paper
the constraint violation observed for the two variants are investigated. It is
concluded that the $SE\left( 3\right) $ formulation outperforms the $SO\left(
3\right) \times \mathbb{R}^{3}$ formulation if the absolute motions of the
rigid bodies, as part of a constrained MBS, belong to a motion subgroup. In all
other cases both formulations are equivalent. In the latter cases the $SO\left(
3\right) \times \mathbb{R}^{3}$ formulation should be used since the $SE\left(
3\right) $ formulation is numerically more complex, however.
