applied forces and the inertial forces of a mechanical system as it moves through a set of virtual displacements. When considering forces applied to a body in static equilibrium, the principle of least action requires the virtual work of these forces to be zero.

Mathematical treatment

Consider a particle P that moves from a point A to a point B along a trajectory , while a force is applied to it. The work done by the force is given by the integral

where is the differential element along the curve that is the trajectory

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