On the form of the motion equations of the multibody systems with elastic elements

Abstract

In many cases when a study of multi-bodies systems is perform, the hypothesis of rigid elements is considered. In reality the elasticity of the components of the system can be large enough so that the dynamic response can be not only quantitative but also qualitative different. For this reason, in some applications, particularly in the field of robotics and high-speed vehicles, is necessary to consider the elasticity of elements and to use correspondent models. Generally, the multi-bodies systems have a great complexity and the strong non-linearity. To study such system with the classic mechanics theorems is not a practical task because the motion equations have, generally, no analytical solutions. For this reason is necessary to use numerical methods and the finite element methods (FEM) remains one of the most important tools.