Virtual displacement

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In analytical mechanics the concept of a virtual displacement, related to the concept of virtual work, is meaningful only when discussing a physical system subject to constraints on its motion. A special case of an infinitesimal displacement (usually notated ), a virtual displacement (notated ) refers to an infinitesimal change in the position coordinates of a system such that the constraints remain satisfied.

For example, if a bead is constrained to move on a hoop, its position may be represented by the position coordinate θ, which gives the angle at which the bead is situated. Say that the bead is at the top. Moving the bead straight upwards from its height z to a height z + dz would represent one possible infinitesimal displacement, but would violate the constraint. The only possible virtual displacement would be a displacement from the bead's position, θ to a new position θ + δθ (where δθ could be positive or negative).

It is also worthwhile to note that virtual displacements are spatial displacements exclusively - time is fixed while they occur. When computing virtual differentials of quantities that are functions of space and time coordinates, no dependence on time is considered (formally equivalent to saying δt = 0).