Static and dynamic aspects of the principle of virtual work

The paper presents a detailed analysis of the principle of virtual work in its statics and dynamics aspects. Special attention is paid to not exact formulation and interpretation of mechanical system motion equations based upon this principle, what is presented quite often in text books. The general form of the principle of virtual work and variational formulations of the problems in statics are presented and analyzed. Additionally, the dynamic implications of the principle of virtual work and dynamics problem formulation of a system subjected to scleronomic constraints are detailed. The basis for the formulation is the dynamic implication of the principle of virtual work that specifies the relation between the constraint reactions and the body accelerations. This relation takes the form of the variation inequality. As the result, the Gauss principle which determines the body acceleration vector is presented. Furthermore, a description of impact formulation, based upon the Carnot model, caused by the constraints is provided. The theoretical development is illustrated with examples of applications of the principle of virtual work.