[QUE/CM-03009]

Let the Lagrangian for a system be invariant, up to a total time derivative, under the transformations $$ q_k \rightarrow q_k^{\,\prime} = q_k + \delta q_k. $$ Assume that  there exists a function  $\Omega $ such that $$  L^\prime(\dot{q}_k^{\,\prime} , q_k^{\,\prime} ,t)= L( \dot{q}_k, q_k, t) + {d\Omega \over dt} . $$ Show that there exists a conserved quantity and find its expression.