Virtual displacement: Given a system in equilibrium, its virtual displacement is imagined as follows: Move the system slightly away from its equilibrium position arbitrarily but consistent with the constraints. This represents a virtual displacement of the system.
Virtual displacement is denoted by 
to distinguish it from a real displacement 
.
Virtual work: The work done by any force 
during a virtual displacement is called virtual work. It is denoted by 
. Thus
Work done by a constraint force is usually zero, implies that virtual work done by a constraint force is also zero. Also keep in mind that in calculating the work 
done by the force 
represents the displacement of the point where the force is being applied.
Principle of virtual work: The necessary and sufficient condition for equilibrium of a mechanical system without friction is that the virtual work done by the externally applied forces is zero.
For a system in equilibrium, each particle in the system is in equilibrium under the influence of externally applied forces and the forces of constraints.
For the ith particle:
For a system of composed of many subsystems:
Net virtual work done by constraint forces is zero. This means that the total virtual work done by the external forces vanishes.
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