| 翻訳と辞書 |
| Buckingham Pi theorem ： ウィキペディア英語版 |
Buckingham π theorem
In engineering, applied mathematics, and physics, the Buckingham theorem is a key theorem in dimensional analysis. It is a formalization of Rayleigh's method of dimensional analysis. Loosely, the theorem states that if there is a physically meaningful equation involving a certain number ''n'' of physical variables, then the original equation can be rewritten in terms of a set of ''p'' = ''n'' − ''k'' dimensionless parameters 1, 2, ..., p constructed from the original variables. (Here ''k'' is the number of physical dimensions involved; it is obtained as the rank of a particular matrix.)
The theorem can be seen as a scheme for nondimensionalization because it provides a method for computing sets of dimensionless parameters from the given variables, even if the form of the equation is still unknown.
== Historical information ==
Although named for Edgar Buckingham, the theorem was first proved by French mathematician J. Bertrand in 1878. Bertrand considered only special cases of problems from electrodynamics and heat conduction, but his article contains in distinct terms all the basic ideas of the modern proof of the theorem and clear indication of its utility for modelling physical phenomena. The technique of using the theorem (“the method of dimensions”) became widely known due to the works of Rayleigh (the first application of the theorem ''in the general case''〔When in applying the pi–theorem there arises an ''arbitrary function'' of dimensionless numbers.〕 to the dependence of pressure drop in a pipe upon governing parameters probably dates back to 1892, a heuristic proof with the use of series expansion, to 1894〔Second edition of ``The Theory of Sound’’().〕).
Formal generalization of the theorem for the case of arbitrarily many quantities was given first by A. Vaschy in 1892,〔Quotes from Vaschy’s article with his statement of the pi–theorem can be found in: 〕 then in 1911—apparently independently—by both A. Federman,〔 (Federman A., On some general methods of integration of first-order partial differential equations, Proceedings of the Saint-Petersburg polytechnic institute. Section of technics, natural science, and mathematics)〕 and D. Riabouchinsky, and again in 1914 by Buckingham.〔(Original text of Buckingham’s article in ''Physical Review'' )〕 It was Buckingham's article that introduced the use of the symbol "''i''" for the dimensionless variables (or parameters), and this is the source for the theorem's name.
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「Buckingham π theorem」の詳細全文を読む
スポンサード リンク
| 翻訳と辞書 : 翻訳のためのインターネットリソース |
Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.
|
|