Zusammenfassung
We show that if a Lagrangian is invariant under a transformation (with the
invariance defined in the standard manner), then the equations of motion
obtained from it maintain their form under the transformation. We also show
that the converse is not true, giving examples of equations of motion that are
form-invariant under a transformation, but these equations can be derived from
a Lagrangian that is not invariant under such transformation. The conclusions
are valid for discrete or continuous systems.
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