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Show that if two Lagrangians for a system $L_1$ and $L_2$ differ by a total time derivative, $$ L_2 = L_1 + \frac{d \Omega}{ dt} $$ , the equations of motion given by them are the same. Consider the case when $\Omega$ depends on the coordinates $q_k$ only and not the generalized velocities $\dot{q}_k$
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