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Virtual work arises in the application of the ''principle of least action'' to the study of forces and movement of a mechanical system. The work of a force acting on a particle as it moves along a displacement will be different for different displacements. Among all the possible displacements that a particle may follow, called virtual displacements, one will minimize the action, and, therefore, is the one followed by the particle by the principle of least action. The work of a force on a particle along a virtual displacement is known as the virtual work. Historically, virtual work and the associated calculus of variations were formulated to analyze systems of rigid bodies,〔(C. Lánczos, The Variational Principles of Mechanics, 4th Ed., General Publishing Co., Canada, 1970 )〕 but they have also been developed for the study of the mechanics of deformable bodies.〔Dym, C. L. and I. H. Shames, ''Solid Mechanics: A Variational Approach'', McGraw-Hill, 1973.〕 == History == The introduction of virtual work and the principle of least action was guided by the view that the actual movement of a body is the one in a set of "tentative" realities that minimizes a particular quantity. This idea that nature minimizes is a version of the "simplicity hypothesis" that can be traced to Aristotle.〔(W. Yourgrau and S. Mandelstam, Variational Principles in Dynamics and Quantum Theory, 3rd Ed., General Publishing Co., Canada, 1968 )〕 Another form of this hypothesis is Occam's razor which states that "it is futile to employ many principles when it is possible to employ fewer." These ideas illustrate a view of physics that nature optimizes in some way. Gottfried Leibniz formulated Newton's laws of motion in terms of work and kinetic energy, or ''vis viva'' (living force), which are minimized as a system moves.〔〔 Maupertuis adapted Leibniz's ideas as the ''principle of least action'' that nature minimizes action. But it was Euler and Lagrange who provided the mathematical foundation of the calculus of variations and applied it to the study of the statics and dynamics of mechanical systems. Hamilton's reformulation of the principle of least action and Lagrange's equations yielded a theory of dynamics that is the foundation for modern physics and quantum mechanics. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Virtual work」の詳細全文を読む スポンサード リンク
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