Question

What's the Physical significance of Lagrangian ?

Answer 1

Hint: Lagrangian theory is a formalism in classical theory . it's the field-theoretic analogue of Lagrangian mechanics. Lagrangian mechanics is employed to research the motion of a system of discrete particles each with a finite number of degrees of freedom.

Complete answer:
In mechanics, the Lagrangian function is simply the K.E. which is that the energy of motion minus the P.E. i.e. energy of position. The mechanics may be a reformulation of Newtonian mechanics , introduced by the Italian-French mathematician and astronomer Joseph-Louis Lagrange within the year 1788. Simply put, if you recognize the Lagrangian for a classical system, then you'll compute exactly how the system behaves.

The Lagrangian formulation of Newtonian mechanics essentially turns the study of classical mechanical systems (such as a system of coupled, massive point-particles, pendula, space rockets, etc) into a minimisation problem. The Lagrangian formulation of Newtonian mechanics shouldn't be thought of as more fundamental than the quality formalism. There isn’t anything more physically significant than a few Lagrangian than the dynamics it describes.

Note: For conservative systems, there's a chic formulation of Newtonian mechanics referred to as the Lagrangian formulation. The Lagrangian function, L, for a system is defined to be the difference between the kinetic and potential energies expressed as a function of positions and velocities.