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In analytical mechanics, a branch of applied mathematics and physics, a virtual displacement δ γ {\displaystyle \delta \gamma } shows how the mechanical system's trajectory can hypothetically deviate very slightly from the actual trajectory γ {\displaystyle \gamma } of the system without violating the system's constraints. For every time instant t , {\displaystyle t,} δ γ {\displaystyle \delta \gamma } is a vector tangential to the configuration space at the point γ . {\displaystyle \gamma.} The vectors δ γ {\displaystyle \delta \gamma } show the directions in which γ {\displaystyle \gamma } can "go" without breaking the constraints.
For example, the virtual displacements of the system consisting of a single particle on a two-dimensional surface fill up the entire tangent plane, assuming there are no additional constraints.
If, however, the constraints require that all the trajectories γ {\displaystyle \gamma } pass through the given point q {\displaystyle \mathbf {q} } at the given time τ , {\displaystyle \tau ,} i.e. γ = q , {\displaystyle \gamma =\mathbf {q} ,} then δ γ = 0. {\displaystyle \delta \gamma =0.}