Lagrangian mechanics is a formulation of classical physics that simplifies the description of the motion of a physical system by using energy concepts rather than forces. It determines the equations of motion by employing the principle of least action, which states that the path taken by a physical system between two points is the path that minimizes the action integral. This formulation relies on the construction of the Lagrangian, which is defined as the difference between the system's kinetic energy and its potential energy. By applying the Euler-Lagrange equations to this Lagrangian, the complex vector calculus required in Newtonian mechanics can be translated into a set of scalar differential equations. This powerful mathematical framework is useful for analyzing coupled oscillations and systems where the constraints are complex, providing a fundamental approach to analytical dynamics in physical sciences.