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.
S = ∫ L dt
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...?[/B]