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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 Scleronomous constraint ： ウィキペディア英語版 Scleronomous A mechanical system is scleronomous if the equations of constraints do not contain the time as an explicit variable. Such constraints are called scleronomic constraints. ==Application== :Main article：Generalized velocity In 3-D space, a particle with mass $m\backslash ,\backslash !$, velocity $\backslash mathbf\backslash ,\backslash !$ has kinetic energy :$T\; =\backslash fracm\; v^2\; \backslash ,\backslash !.$ Velocity is the derivative of position with respect to time. Use chain rule for several variables: :$\backslash mathbf=\backslash frac=\backslash sum\_i\backslash \; \backslash frac\backslash dot\_i+\backslash frac\backslash ,\backslash !.$ Therefore, :$T\; =\backslash fracm\; \backslash left(\backslash sum\_i\backslash \; \backslash frac\backslash dot\_i+\backslash frac\backslash right)^2\backslash ,\backslash !.$ Rearranging the terms carefully, :$T\; =T\_0+T\_1+T\_2\backslash ,\backslash !:$ :$T\_0=\backslash fracm\backslash left(\backslash frac\backslash right)^2\backslash ,\backslash !,$ :$T\_1=\backslash sum\_i\backslash \; m\backslash frac\backslash cdot\; \backslash frac\backslash dot\_i\backslash ,\backslash !,$ :$T\_2=\backslash sum\_\backslash \; \backslash fracm\backslash frac\backslash cdot\; \backslash frac\backslash dot\_i\backslash dot\_j\backslash ,\backslash !,$ where $T\_0\backslash ,\backslash !$, $T\_1\backslash ,\backslash !$, $T\_2\backslash ,\backslash !$ are respectively homogeneous functions of degree 0, 1, and 2 in generalized velocities. If this system is scleronomous, then the position does not depend explicitly with time: :$\backslash frac=0\backslash ,\backslash !.$ Therefore, only term $T\_2\backslash ,\backslash !$ does not vanish: :$T\; =\; T\_2\backslash ,\backslash !.$ Kinetic energy is a homogeneous function of degree 2 in generalized velocities . 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「Scleronomous」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.