The original vector equation could be recovered by recognizing that the work expression must hold for arbitrary displacements. Separating the total forces into applied forces, F i , and constraint forces, C i , yields δ δ W = ∑ ∑ i F i ⋅ ⋅ δ δ r i + ∑ ∑ i C i ⋅ ⋅ δ δ r i − − ∑ ∑ i m i a i ⋅ ⋅ δ δ r i = 0.