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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 Liouville dynamical system ： ウィキペディア英語版 Liouville dynamical system In classical mechanics, a Liouville dynamical system is an exactly soluble dynamical system in which the kinetic energy ''T'' and potential energy ''V'' can be expressed in terms of the ''s'' generalized coordinates ''q'' as follows: :$$ T = \frac \left\) + u_(q_) + \cdots + u_(q_) \right\} \left\) \dot_^ + v_(q_) \dot_^ + \cdots + v_(q_) \dot_^ \right\} :$$ V = \frac) + w_(q_) + \cdots + w_(q_) }) + u_(q_) + \cdots + u_(q_) } The solution of this system consists of a set of separably integrable equations :$$ \frac\, dt = \frac - \omega_ + \gamma_}} = \frac - \omega_ + \gamma_}} = \cdots = \frac - \omega_ + \gamma_}} where ''E = T + V'' is the conserved energy and the $\backslash gamma\_$ are constants. As described below, the variables have been changed from ''qs'' to φs, and the functions ''us'' and ''ws'' substituted by their counterparts ''χs'' and ''ωs''. This solution has numerous applications, such as the orbit of a small planet about two fixed stars under the influence of Newtonian gravity. The Liouville dynamical system is one of several things named after Joseph Liouville, an eminent French mathematician. ==Example of bicentric orbits== In classical mechanics, Euler's three-body problem describes the motion of a particle in a plane under the influence of two fixed centers, each of which attract the particle with an inverse-square force such as Newtonian gravity or Coulomb's law. Examples of the bicenter problem include a planet moving around two slowly moving stars, or an electron moving in the electric field of two positively charged nuclei, such as the first ion of the hydrogen molecule H2, namely the hydrogen molecular ion or H2+. The strength of the two attractions need not be equal; thus, the two stars may have different masses or the nuclei two different charges. 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「Liouville dynamical system」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.