Virtual Work - Explanation

Explanation

If a force acts on a particle as it moves from point A to point B, then, for each possible trajectory that the particle may take, it is possible to compute the total work done by the force along the path. The principle of virtual work, which is the form of the principle of least action applied to these systems, states that the path actually followed by the particle is the one for which the difference between the work along this path and other nearby paths is zero. The formal procedure for computing the difference of functions evaluated on nearby paths is a generalization of the derivative known from differential calculus, and is termed the calculus of variations.

Let the function x(t) define the path followed by a point. A nearby path can then be defined by adding the function δx(t) to the original path, so that the new path is given by x(t)+δx(t). The function δx(t) is called the variation of the original path, and each of the components of δx=(δx, δy, δz) is called a virtual displacement. This can be generalized to an arbitrary mechanical system defined by the generalized coordinates q_i, i=1,..., n. In which case, the variation of the trajectory q_i(t) is defined by the virtual displacements δq_i, i=1,..., n.

Virtual work can now be described as the work done by the applied forces and the inertial forces of a mechanical system as it moves through a set of virtual displacements.