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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 Free motion equation ： ウィキペディア英語版 Free motion equation A free motion equation is a differential equation that describes a mechanical system in the absence of external forces, but in the presence only of an inertial force depending on the choice of a reference frame. In non-autonomous mechanics on a configuration space $Q\backslash to\; \backslash mathbb\; R$, a free motion equation is defined as a second order non-autonomous dynamic equation on $Q\backslash to\; \backslash mathbb\; R$ which is brought into the form : $\backslash overline\; q^i\_=0$ with respect to some reference frame $(t,\backslash overline\; q^i)$ on $Q\backslash to\; \backslash mathbb\; R$. Given an arbitrary reference frame $(t,q^i)$ on $Q\backslash to\; \backslash mathbb\; R$, a free motion equation reads : $q^i\_=d\_t\backslash Gamma^i\; +\backslash partial\_j\backslash Gamma^i(q^j\_t-\backslash Gamma^j)\; -$ \frac\frac(q^j_t-\Gamma^j) (q^k_t-\Gamma^k), where $\backslash Gamma^i=\backslash partial\_t\; q^i(t,\backslash overline\; q^j)$ is a connection on $Q\backslash to\; \backslash mathbb\; R$ associates with the initial reference frame $(t,\backslash overline\; q^i)$. The right-hand side of this equation is treated as an inertial force. A free motion equation need not exist in general. It can be defined if and only if a configuration bundle $Q\backslash to\backslash mathbb\; R$ of a mechanical system is a toroidal cylinder $T^m\backslash times\; \backslash mathbb\; R^k$. == References == * De Leon, M., Rodrigues, P., Methods of Differential Geometry in Analytical Mechanics (North Holland, 1989). * Giachetta, G., Mangiarotti, L., Sardanashvily, G., Geometric Formulation of Classical and Quantum Mechanics (World Scientific, 2010) ISBN 981-4313-72-6 ((arXiv: 0911.0411 )). 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「Free motion equation」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.