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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 Nambu mechanics ： ウィキペディア英語版 Nambu mechanics In mathematics, Nambu dynamics is a generalization of Hamiltonian mechanics involving multiple Hamiltonians. Recall that Hamiltonian mechanics is based upon the flows generated by a smooth Hamiltonian over a symplectic manifold. The flows are symplectomorphisms and hence obey Liouville's theorem. This was soon generalized to flows generated by a Hamiltonian over a Poisson manifold. In 1973, Yoichiro Nambu suggested a generalization involving Nambu-Poisson manifolds with more than one Hamiltonian. == Nambu bracket == Specifically, consider a differential manifold , for some integer ; one has a smooth -linear map from copies of to itself, such that it is completely antisymmetric: the Nambu bracket, :$\backslash \; :\; C^\backslash infty(M)\; \backslash times\; \backslash cdots\; C^\backslash infty(M)\; \backslash rightarrow\; C^\backslash infty(M),$ which acts as a derivation :$\backslash \; =\; \backslash g\; +\; f\backslash ,$ whence the Filippov Identities (FI), (evocative of the Jacobi identities, but unlike them, ''not'' antisymmetrized in all arguments, for ): $\backslash \backslash \}\; =\; \backslash ,~g\_2,\backslash cdots,~g\_N\backslash \}+\backslash ,\backslash cdots,g\_N\backslash \}+\backslash dots$ $+\backslash ,~g\_N\backslash \}\backslash \},$ so that acts as a generalized derivation over the -fold product . 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「Nambu mechanics」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.