Energy and Symmetry-Preserving Formulation of Nonlinear Constraints and Potential Forces in Multibody Dynamics

Abstract

Many mechanical problems are adequately represented by models composed by different elements such as particles, rigid and deformable bodies. Geometric integrators, designed to provide numerical solutions that exactly inherit basic features of the underlying time-continuous model. The concept of discrete derivative [1, 2] plays a central role in the systematic design of a EM method. Interestingly, its particular expression is not unique and accordingly several formulations have been proposed in the literature for our systems of interest. The main result is that just one of the reviewed discrete derivatives generally complies with the requirements of a EM method, while the others do so only in particular cases.