A New Representation for the Dynamics of Rigid Bodies

Abstract

The dynamics of a rigid body can be described from either a Lagrangian or an Eulerian perspective. The Lagrangian description is the most common in the literature on the rigid body dynamics. It follows individual particles attached to the body, such as the center of mass. In contrast, the Eulerian approach tracks the flow of rigid body particles through a fixed location in space. Although this approach is uncommon in the rigid body literature, it can be helpful in certain cases. Therefore, in this article, we use the Eulerian approach to develop a new formulation for rigid body dynamics, employing the velocities of a spatial point as generalized velocities. This point is not fixed to the body. It is always located through a vector that is constant in the global inertial frame, originating from the center of mass of the body. Thus, at any instant, the spatial point coincides with a material point fixed to the body and has the same velocity. The validity of this formulation for modeling the three-dimensional motion of a rigid body is demonstrated through an example. Furthermore, it is shown in a practical case that the proposed formulation can be useful for unilateral contact problems.