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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Mechanical similarity ： ウィキペディア英語版 Mechanical similarity In classical mechanics, a branch overlapping in physics and applied mathematics, mechanical similarity occurs when the potential energy is a homogeneous function of the positions of the particles, with the result that the trajectories of the particles in the system are geometrically similar paths, differing in size but retaining shape. Consider a system of any number of particles and assume that the interaction energy between any pair of particles has the form :$U(r)\backslash propto\; r^k\; \backslash ,,$ where ''r'' is the distance between the two particles. In such a case the solutions to the equations of motion are a series of geometrically similar paths, and the times of motion ''t'' at corresponding points on the paths are related to the linear size ''l'' of the path by :$t\; \backslash propto\; l^.$ ==Examples== * The period of small oscillations (''k'' = 2) is independent of their amplitude. * The time of free fall under gravity (''k'' = 1) is proportional to the square root of the initial altitude. * The square of the time of revolution of the planets (''k'' = −1) is proportional to the cube of the orbital size. 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「Mechanical similarity」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.