2, ..., n are the applied forces and applied moments, respectively, and ?r_i , i = 1, 2, ..., m and ?'?_j, j = 1, 2, ..., n are the virtual displacements and virtual rotations, respectively.

Suppose the system consists of N particles, and it has f (f <= 6N) degrees of freedom. It is sufficient to use only f coordinates to give a complete description of the motion of the system, so f generalized coordinates q_k , k = 1, 2, ..., f are defined such that the virtual movements can be expressed in terms of these generalized coordinates. That is,