Principle of stationary action

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

Pierre Maupertuis stated in 1746 that many processes in nature are either optimal, or they take extreme values. This is known as the principle of stationary action and is a part of mechanics. It states that physical fields and particles will sometimes take extreme values (which are maximal or minimal). For this reason, it is often called principle of least action. Maupertuis gives a way to determine equations of motion when looking at the action of a mechanical system.


One of the first to formulate this was Pierre de Fermat. In the 1600s, he wrote: "light travels between two given points along the path of shortest time".

Maupertuis wrote: "The laws of movement and of rest deduced from this principle being precisely the same as those observed in nature, we can admire the application of it to all phenomena. The movement of animals, the vegetative growth of plants ... are only its consequences; and the spectacle of the universe becomes so much the grander, so much more beautiful, the worthier of its Author, when one knows that a small number of laws, most wisely established, suffice for all movements."

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