He is often credited with having invented the principle of least action; a version is known as Maupertuis'principle & ndash; an integral equation that determines the path followed by a physical system.
32.
It is a modification of the Hamilton Jacobi equation ( HJE ) from classical mechanics, and can be derived from the Einstein Hilbert action using the principle of least action in the ADM formalism.
33.
In contrast, the governments taking the least action against it are North Korea, Iran, Eritrea, Equatorial Guinea, Hong Kong, Central African Republic, Papua New Guinea, Guinea, the Democratic Republic of the Congo and South Sudan.
34.
This problem is conceptually related to the principle of least action in physics, in that it can be restated : what is the principle of action which encloses the greatest area, with the greatest economy of effort?
35.
Hence the principle of least action is not just the culmination of Maupertuis s work in several areas of physics, he sees it as his most important achievement in philosophy too, giving an incontrovertible proof of God.
36.
Maupertuis was the first to publish a " principle of least action ", where he defined " action " as \ int v \, ds, which was to be minimized over all paths connecting two specified points.
37.
His expression corresponds to what we would now call potential energy, so that his statement of least action in statics is equivalent to the principle that a system of bodies at rest will adopt a configuration that minimizes total potential energy.
38.
Thus, Maupertuis takes credit for conceiving the principle of least action as a " general " principle applicable to all physical systems ( not merely to light ), whereas the historical evidence suggests that Euler was the one to make this intuitive leap.
39.
In 1751, Maupertuis'priority for the principle of least action was challenged in print ( " Nova Acta Eruditorum " of Leipzig ) by an old acquaintance, Johann Samuel Koenig, who quoted a 1707 letter purportedly from Frederick II were engaged in the quarrel.
40.
This plays a role similar to that of the Schr�dinger equation in non-relativistic quantum mechanics, but a Lagrangian is not an equation of motion rather, it is a polynomial function of the fields and their derivatives, and used with the principle of least action.
