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Hooke's law is a principle of physics that states that the force needed to extend or compress a spring by some distance is proportional to that distance. That is: , where is a constant factor characteristic of the spring, its stiffness. The law is named after 17th century British physicist Robert Hooke. He first stated the law in 1660 as a Latin anagram.〔The anagram was given in alphabetical order, ''ceiiinosssttuv'', representing ''Ut tensio, sic vis'' — "As the extension, so the force": 〕〔See (), where one can find also an anagram for the catenary.〕 He published the solution of his anagram in 1678 as: ''ut tensio, sic vis'' ("as the extension, so the force" or "the extension is proportional to the force"). Hooke's equation in fact holds (to some extent) in many other situations where an elastic body is deformed, such as wind blowing on a tall building, a musician plucking a string of a guitar, or the filling of a party balloon. An elastic body or material for which this equation can be assumed is said to be linear-elastic or Hookean. Hooke's law is only a first order linear approximation to the real response of springs and other elastic bodies to applied forces. It must eventually fail once the forces exceed some limit, since no material can be compressed beyond a certain minimum size, or stretched beyond a maximum size, without some permanent deformation or change of state. In fact, many materials will noticeably deviate from Hooke's law well before those elastic limits are reached. On the other hand, Hooke's law is an accurate approximation for most solid bodies, as long as the forces and deformations are small enough. For this reason, Hooke's law is extensively used in all branches of science and engineering, and is the foundation of many disciplines such as seismology, molecular mechanics and acoustics. It is also the fundamental principle behind the spring scale, the manometer, and the balance wheel of the mechanical clock. The modern theory of elasticity generalizes Hooke's law to say that the strain (deformation) of an elastic object or material is proportional to the stress applied to it. However, since general stresses and strains may have multiple independent components, the "proportionality factor" may no longer be just a single real number, but rather a linear map (a tensor) that can be represented by a matrix of real numbers. In this general form, Hooke's law makes it possible to deduce the relation between strain and stress for complex objects in terms of intrinsic properties of the materials it is made of. For example, one can deduce that a homogeneous rod with uniform cross section will behave like a simple spring when stretched, with a stiffness directly proportional to its cross-section area and inversely proportional to its length. ==Formal definition== 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「Hooke's law」の詳細全文を読む スポンサード リンク
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