These last terms, evaluated around the endpoints t 0 and t 1 , should cancel each other in order to make the total change in the action Δ Δ S be zero, as would be expected if the trajectory is a solution. That is ( ∂ ∂ L ∂ ∂ q ˙ ˙ φ φ ) ( t 0 ) = ( ∂ ∂ L ∂ ∂ q ˙ ˙ φ φ ) ( t 1 ) , meaning the quantity ( ∂ ∂ L / ∂ ∂ q ˙ ˙ ) φ φ is conserved, which is the conclusion of Noether's theorem. For instance if pure translations of q by a constant are the symmetry, then the conserved quantity becomes just ( ∂ ∂ L / ∂ ∂ q ˙ ˙ ) = p , the canonical momentum.