In this paper, the extended reduced order physical model, which is developed to represent dynamics of flexible structures in multibody systems, is implemented to general multibody formulations. The elastic deformations are described using vibration modes associated with the rigid bodies that are effectively defined using dynamic properties of the system in this reduced order modeling method. The recursive formulation and the augmented formulation are used to develop the constraint equations associated with the connections between the reference body and the several rigid bodies in the modal representations used to modal elastic deformations. For this purpose, the n-body constraint is developed for the recursive formulations, while these constraint equations are transformed into the form that is suitable for the augmented formulation using the singular value decomposition or QR decomposition. The use of the formulations in this paper allows for the implementation of the extended reduced order physical model into the commercial multibody codes such as SIMPACK, ADAMS, and DADS.

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