In analytical mechanics, a branch of applied mathematics and physics, a virtual displacement (or infinitesimal variation) δ δ γ γ shows how the mechanical system's trajectory can hypothetically (hence the term virtual) deviate very slightly from the actual trajectory γ γ of the system without violating the system's constraints. For every time instant t , δ δ γ γ ( t ) is a vector tangential to the configuration space at the point γ γ ( t ) . The vectors δ δ γ γ ( t ) show the directions in which γ γ ( t ) can "go" without breaking the constraints.