I'm studying lagrangian mechanics, and there's a property where you could obtain an equivalent lagrangian $\mathcal{L'}$ from $\mathcal{L}$ by adding a function which satisfies: $$ \mathcal{L'}\rightarrow \mathcal{L}+\frac{df(q,t)}{dt}.$$ This lagrangian $L'$ would give rise to the same equations...