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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 Hamiltonian fluid mechanics ： ウィキペディア英語版 Hamiltonian fluid mechanics Hamiltonian fluid mechanics is the application of Hamiltonian methods to fluid mechanics. This formalism can only apply to nondissipative fluids. ==Irrotational barotropic flow== Take the simple example of a barotropic, inviscid vorticity-free fluid. Then, the conjugate fields are the mass density field ''ρ'' and the velocity potential ''φ''. The Poisson bracket is given by :$()=\backslash delta^d(\backslash vec-\backslash vec)$ and the Hamiltonian by: :$\backslash mathcal=\backslash int\; \backslash mathrm^d\; x\; \backslash left(\; \backslash frac\backslash rho(\backslash nabla\; \backslash varphi)^2\; +e(\backslash rho)\; \backslash right),$ where ''e'' is the internal energy density, as a function of ''ρ''. For this barotropic flow, the internal energy is related to the pressure ''p'' by: :$e\text{'}\text{'}\; =\; \backslash fracp\text{'},$ where an apostrophe ('), denotes differentiation with respect to ''ρ''. This Hamiltonian structure gives rise to the following two equations of motion: :$$ \begin \frac&=+\frac= -\nabla \cdot(\rho\vec), \\ \frac&=-\frac=-\frac\vec\cdot\vec-e', \end where $\backslash vec\backslash \; \backslash stackrel\backslash \; \backslash nabla\; \backslash varphi$ is the velocity and is vorticity-free. The second equation leads to the Euler equations: :$\backslash frac\; +\; (\backslash vec\backslash cdot\backslash nabla)\; \backslash vec\; =\; -e\text{'}\text{'}\backslash nabla\backslash rho\; =\; -\backslash frac\backslash nabla$ after exploiting the fact that the vorticity is zero: :$\backslash nabla\; \backslash times\backslash vec=\backslash vec.$ As fluid dynamics is described by non-canonical dynamics, which possess an infinite amount of Casimir invariants, an alternative formulation of Hamiltonian formulation of fluid dynamics can be introduced through the use of Nambu mechanics 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「Hamiltonian fluid 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.