That changes the Lagrangian by Δ Δ L ≈ ≈ ( ∂ ∂ L / ∂ ∂ q ˙ ˙ ) Δ Δ q ˙ ˙ , which integrates to Δ Δ S = ∫ ∫ Δ Δ L ≈ ≈ ∫ ∫ ∂ ∂ L ∂ ∂ q ˙ ˙ Δ Δ q ˙ ˙ ≈ ≈ ∫ ∫ ∂ ∂ L ∂ ∂ q ˙ ˙ ( ± ± δ δ q τ τ ) ≈ ≈ ± ± ∂ ∂ L ∂ ∂ q ˙ ˙ δ δ q = ± ± ∂ ∂ L ∂ ∂ q ˙ ˙ φ φ .