Editing Virtual work (section)

== History ==
The '''principle of virtual work''' had always been used in some form since antiquity in the study of statics. It was used by the Greeks, medieval Arabs and Latins, and Renaissance Italians as "the law of lever".<ref name=capecchi>{{cite book | last=Capecchi | first=Danilo | title=History of Virtual Work Laws | series=Science Networks. Historical Studies | publisher=Springer Milan | location=Milano | year=2012 | volume=42 | isbn=978-88-470-2055-9 | doi=10.1007/978-88-470-2056-6 }}</ref> The idea of virtual work was invoked by many notable physicists of the 17th century, such as Galileo, Descartes, Torricelli, Wallis, and Huygens, in varying degrees of generality, when solving problems in statics.<ref name=capecchi/> Working with Leibnizian concepts,  [[Johann Bernoulli]] systematized the virtual work principle and made explicit the concept of infinitesimal displacement. He was able to solve problems for both rigid bodies as well as fluids. Bernoulli's version of virtual work law appeared in his letter to [[Pierre Varignon]] in 1715, which was later published in Varignon's second volume of ''Nouvelle mécanique ou Statique'' in 1725. This formulation of the principle is today known as the principle of virtual velocities and is commonly considered as the prototype of the contemporary virtual work principles.<ref name=capecchi/> In 1743 D'Alembert published his ''Traité de Dynamique'' where he applied the principle of virtual work, based on Bernoulli's work, to solve various problems in dynamics. His idea was to convert a dynamical problem into static problem by introducing ''inertial force''.<ref name=dugas>René Dugas, A History of Mechanics, Courier Corporation, 2012</ref> In 1768, [[Lagrange]] presented the virtual work principle in a more efficient form by introducing generalized coordinates and presented it as an alternative principle of mechanics by which all problems of equilibrium could be solved. A systematic exposition of Lagrange's program of applying this approach to all of mechanics, both static and dynamic, essentially [[D'Alembert's principle]], was given in his ''Mécanique Analytique'' of 1788.<ref name=capecchi/> Although Lagrange had presented his version of [[least action principle]] prior to this work, he recognized the virtual work principle to be more fundamental mainly because it could be assumed alone as the foundation for all mechanics, unlike the modern understanding that least action does not account for non-conservative forces.<ref name=capecchi/>