The Lagrangian function also termed as Lagrangian, is the quantity that characterizes the state of a physical system. In mechanics, the Lagrangian function is just the kinetic energy which is the energy of motion minus the potential energy i.e. energy of position. The mechanics is a reformulation of classical mechanics, introduced by the Italian-French mathematician and astronomer Joseph-Louis Lagrange in the year 1788. Simply put, if you know the Lagrangian for a classical system, then you can work out exactly how the system behaves.