I am new to lagrangian mechanics and it just baffles me the idea of subtracting potential energy from kinetic energy. Why don't we use kinetic energy alone and the least action path (between two points) would be the one with lowest kinetic energy integral (with respect to any possible variation)?
Note:
what i understand is that potential energy is the work whcih "will" be done if the object observed is to finish its motion and kinetic energy is the work done already by the force. So subtracting them doesn't give me a good intuition about lagrangian.
i know that there are other answers on stack, but they just derive the equations mathematically, i want a more intuitive approach (what the equation in itself means and how it differes from a path to another i,e if the path becomes longer ,greater in energy than least action, how would the value change?)
