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## Main Question or Discussion Point

what is the reason that the lagrangian remains invariant under addition of an arbtrary function of time???

- Thread starter preet0283
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what is the reason that the lagrangian remains invariant under addition of an arbtrary function of time???

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It is the equations of motion that are invariant under the addition of a function that is the total time derivative of some function, to the Lagrangian. Since the Euler-Lagrange equations involve derivatives with respect to position and velocity only, a partial derivative wrt to position or velocity of this added function will be zero.

Hope this helps

Ray

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MalleusScientiarum

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