In the Lagrangian formulation of Classical Mechanics, we have the freedom to add a total time derivative of an arbitrary function $\Lambda$ to the Lagrangian:
$$ L \to L + \frac{d \Lambda}{dt} . $$
Does this symmetry of the Lagrangian have any particular name?
Answer
Some authors call that a gauge transformation of the Lagrangian function. Others, don't give any specific name and may object to the previous one.
For a reference for the former denomination, see for instance F. Scheck, Mechanics, Springer, 2010.
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