In multibody systems, mechanical components (bodies) can be assumed rigid (non-deformable), if their deformation is negligible. For components with non-negligible deformations several methods were developed to represent their deformation. The most widely used method is the floating frame of reference. In this formulation the deformable body is represented by a finite element model whose deformation is described with respect to a local body-fixed frame. Unfortunately, finite element models can include many degrees-of-freedom, which stand in contradiction to the requirements of multibody dynamics. System truncation is therefore inevitable to support computational efficiency. The use of modal data in representing a deformable body is well understood in the multibody community. By truncating modes associated with higher frequencies, the total degrees-of-freedom of the deformable body can be reduced while preserving its dynamic eigen-properties. However, since the finite element model may be in contact with other moving bodies, the reduction technique needs to address the issue of moving boundary conditions. The component mode synthesis reduction methods are such techniques that describe the deflection of all the nodes as a superposition of different types of modes. However, it is limited in the fact that the nodes in contact need to remain in contact throughout a simulation. In some applications these nodes may change, i.e. a node that is in contact with another body or the ground at one instant may become free at the next instant. The present methodologies in multibody modeling of a deformable body with modal data have not yet addressed the issue of changing contact nodes. This research highlights the usefulness of orientation invariant characteristics of some deformable bodies. It proposes to define orientation invariant degrees-of-freedom of the reduced model in Eulerian space, while the remaining degrees-of-freedom are defined in Lagrangian space. In some circumstances, this approach can resolve the issue of changing contact nodes. The combination of Eulerian and Lagrangian formulation for component mode synthesis reduced finite element models is a new concept in deformable multibody dynamics.