# Lagrangian mechanics

In physics, **Lagrangian mechanics** is a formulation of classical mechanics founded on the stationary-action principle (also known as the principle of least action). It was introduced by the Italian-French mathematician and astronomer Joseph-Louis Lagrange in his 1788 work, *Mécanique analytique*.[1]

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Lagrangian mechanics describes a mechanical system as a pair consisting of a configuration space and a smooth function within that space called a *Lagrangian*. For many systems, where and are the kinetic and potential energy of the system, respectively.[2]

The stationary action principle requires that the action functional of the system derived from must remain at a stationary point (a maximum, minimum, or saddle) throughout the time evolution of the system. This constraint allows the calculation of the equations of motion of the system using Lagrange's equations.[3]