1. The problem statement, all variables and given/known data Given L (q, dq/dt, t). translation: q ---> q + e (e is infinitesimal constant) show that if ∂L/∂q = 0, then L is symmetry under the above translation. then find conserved quantity. 2. Relevant equations S = ∫ L dt 3. The attempt at a solution My attempt is nothing... because I don't know the proper procedure to prove a symmetry. Do I simply prove L' - L = 0? But then the next part askes me to find conserved quantity. I have no idea how to find it... So, can anyone spare me some hints...?