EULER, LEONHARD. - ON THE PRINCIPLE OF LEAST ACTION.

Réfléxions sur quelques Loix génerales de la Nature qui s'observent dans les Effets des Forces quelconques. (Reflection on some general laws of nature which are observed in the effects of random forces).

(Berlin, Haude et Spener, 1750). 4to. No wrappers as issued in "Mémoires de l'Academie Royale des Sciences et Belles-Lettres" Tome IV, Année 1748. Pp. (189-) 218 and 1 engraved plate.

First appearance of this paper, in which Euler proves that given the static principle, he can derive the equilibrium conditions for a fluid, and from these, he obtains the integrability conditions for a "Pfaffian" form in three variables. He also looks at the equilibrium of a weight suspended from three elastic cords by looking, via analogy, to a special case of the problem for fluids.

"In his 1748 paper, Euler in "Reflexions sur quelques loix generales de la nature.." starts by declaring his commitment to the least-action principle. His expression corresponds to what we would now call potential energy, so that his statement of least action (formulated by Maupertuis in 1746) in statics is equivalent to the principle that a system of bodies at rest will adopt a configuration that minimizes total potential energy. Euler called this quantity "effort"."

Enestrom: E 146.

Order-nr.: 45871