For small rotations, i.e., α α and β β are ≪ ≪ 1 we have tan ⁡ ⁡ α α ≈ ≈ α α , tan ⁡ ⁡ β β ≈ ≈ β β and, again, for small displacement gradients, we have α α = ∂ ∂ u y ∂ ∂ x , β β = ∂ ∂ u x ∂ ∂ y thus γ γ x y = α α + β β = ∂ ∂ u y ∂ ∂ x + ∂ ∂ u x ∂ ∂ y By interchanging x and y and u x and u y , it can be shown that γ γ x y = γ γ y x .