Principle of virtual work . Short question M.Sc

A virtual displacement is an infinitesimal, imaginary displacement that is consistent with the constraints of the system, and it is considered to occur instantaneously, so that no actual work is done by the forces of constraint.

Mathematically, for a system of particles or rigid bodies, the principle can be expressed as:

δW = Σ Fᵢ · δrᵢ + Σ Mᵢ · δθᵢ = 0

Here, Fᵢ are the external forces, δrᵢ are the corresponding virtual displacements of their points of application, Mᵢ are the external moments, and δθᵢ are the corresponding virtual rotations.

This principle is particularly useful for analyzing complex structures and mechanisms because it allows us to bypass the need to explicitly consider the forces of constraint, which often do no work in a virtual displacement.