section_path: Lagrangian mechanics
section_name: Lagrangian mechanics
paragraph_text: Lagrangian mechanics
  
  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 presentation to the Turin Academy of Science in 1760 culminating in his 1788 grand opus, Mécanique analytique. Lagrangian mechanics describes a mechanical system as a pair (M, L) {\textstyle (M,L)} consisting of a configuration space M {\textstyle M} and a smooth function L {\textstyle L} within that space called a Lagrangian. For many systems, L = T − V, {\textstyle L=T-V,} where T {\textstyle T} and V {\displaystyle V} are the kinetic and potential energy of the system, respectively. The stationary action principle requires that the action functional of the system derived from L {\textstyle L} 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.