If arbitrary virtual displacements are assumed to be in directions that are orthogonal to the constraint forces (which is not usually the case, so this derivation works only for special cases), the constraint forces don't do any work, ∑ ∑ i C i ⋅ ⋅ δ δ r i = 0 . Such displacements are said to be consistent with the constraints. This leads to the formulation of d'Alembert's principle, which states that the difference of applied forces and inertial forces for a dynamic system does no virtual work: δ δ W = ∑ ∑ i ( F i − − m i a i ) ⋅ ⋅ δ δ r i = 0.