Principle of Least Action

Principle of Least Action The principle of least action is a variational principle in physics that relates the minimisation of the action to the equations of motion of a system.

In physics, the principle of least action – or, more accurately, the principle of stationary action – is a variational principle that, when applied to the action of a mechanical system, can be used to obtain the equations of motion for that system. The principle led to the development of the Lagrangian and Hamiltonian formulations of classical mechanics. The principle remains central in modern physics and mathematics, being applied in the theory of relativity, quantum mechanics and quantum field theory, and a focus of modern mathematical investigation in Morse theory. This article deals primarily with the historical development of the idea; a treatment of the mathematical description and derivation can be found in the article on action. The chief examples of the principle of stationary action are Maupertuis' principle and Hamilton's principle.

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