In the field of physics, the Lagrangian term is defined as a scalar function, from which the laws of conservation, temporal evolution and other essential characteristics of a dynamic system can be captured. It is such a significant function that within physics the Lagrangian is the main operator that specifies a physical system.
The Lagrangian is a scalar function described on a space of possible states of the system. The name of this function is due to the astronomer and mathematician Joseph Louis de Lagrange. The notion of a Lagrangian was included by Lagrange himself in a reformulation of classical mechanics in 1778.
In Lagrangian mechanics, the path of an object is obtained by finding the path that reduces the action, which is the integral of the Lagrangian in time.
This reformulation was essential since it was possible to explore the mechanics of alternate systems of Cartesian coordinates, such as: cylindrical, spherical and polar coordinates. The Lagrangian enunciation considerably facilitates many of the physical problems compared to Newton's laws. For example: a bead on a hoop will be studied. If it is decided to calculate the movement of said bead by applying Newtonian mechanics, a complex system of equations would be obtained, which would take into account the forces that the ring exerts on the bead at all times.
While with the Lagrange approximation, you can observe all the possible movements that the account can adopt in the ring, locating mathematically the one that minimizes the action.
