Our aim is now to introduce the concepts of real power and virtual power produced by forces and to present some applications. We first consider the very simple cases of a material point and of a system of material points (Section 4.1). We then study more complex situations (Section 4.2) before finally defining and studying the power of internal forces for a continuum medium in Section 4.3. This eventually leads to the virtual power theorem and to the kinetic energy theorem.

From the standpoint of mechanics, this chapter does not present much new material, but it gives very useful and different perspectives on the concepts and notions already introduced.

Study of a system of material points

Before considering the case of a system of material points, we start by considering that of a single material point. All that we say for a point or even for a system of points is simple and sometimes naive; it is, however, instructive.

The case of a material point

Definition 4.1.For a force F applied to a material point M, the (real) power produced by F at time t and for the given frame of reference is the scalar product F U (U being the velocity of M at time t in the considered frame of reference).