In Lagrangian mechanics, the function L=T-V, called Lagrangian, is introduced. Is there any reason for this quantity to be introduced? Does it have any physical meaning? A professor of mine once said its differential delta L=dT-dV is 'the quantity of energy you must pump into the system to move it from a point (q, dot q) in the phase space to a point (q+dq, dot q+d dot q)'. Is this interpretation correct? I'm not too convinced___________