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comment Lagrangians not of the form $T-U$
He struggled to define it concisely. He merely said that it was an abstract function of generalized coordinates, velocity and time that produced "sensible" equations of motion when Euler-Lagrange equations were calculated. I don't know if he was trying to prepare us for the generalization of the Principle of Least Action to other subject areas or whether he was referring to systems still in the realm of Classical Mechanics.
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