Starting on the topic of the Lagrangian, I have been told not to try to make intuitive sense, but just accept the nice differential equations which it goes into. Fine, but it should at least make basic sense. That L= T-V should be stationary means then d(T-V) = dT-dV = 0, i.e., dT=dV, which translates into that if the kinetic energy increases, then the potential energy increases by the same amount. In what sort of context is this supposed to make sense? Thanks in advance.