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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 Lagrange stability ： ウィキペディア英語版 Lagrange stability Lagrange stability is a concept in the stability theory of dynamical systems, named after Joseph-Louis Lagrange. Consider a real continuous dynamical system $(T,M,\backslash Phi)$, where $T$ is $\backslash mathbb$. For any point in the state space, $x\; \backslash in\; M$, the motion $\backslash Phi(t,x)$ is said to be ''positively Lagrange stable'' if the positive semi-orbit $\backslash gamma\_x^+$ is comapct. If the negative semi-orbit $\backslash gamma\_x^-$ is comapct, then the motion is said to be ''negatively Lagrange stable''. The motion through $x$ is said to be ''Lagrange stable'' if it is both positively and negatively Lagrange stable. If the state space $M$ is the Euclidean space $\backslash mathbb^n$, then the above definitions are equivalent to $\backslash gamma\_x^+,\; \backslash gamma\_x^-$ and $\backslash gamma\_x$ being bounded, respectively. A dynamical system is said to be positively-/negatively-/Lagrange stable if ''for each'' $x\; \backslash in\; M$, the motion $\backslash Phi(t,x)$ is positively-/negativey-/Lagrange stable, respectively. ==Further reading== * Elias P. Gyftopoulos, ''Lagrange Stability and Liapunov's Direct Method''. Proc. of Symposium on Reactor Kinetics and Control, 1963. ((PDF )) * 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「Lagrange stability」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.