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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 Kirchhoff equations ： ウィキペディア英語版 Kirchhoff equations In fluid dynamics, the Kirchhoff equations, named after Gustav Kirchhoff, describe the motion of a rigid body in an ideal fluid. : $$ \begin } & = \times \vec \omega + \vec F_h + \vec F, \\() T & = \left( \vec \omega^T \tilde I \vec \omega + m v^2 \right) \\() \vec Q_h & =-\int p \vec x \times \hat n \, d\sigma, \\() \vec F_h & =-\int p \hat n \, d\sigma \end where $\backslash vec\; \backslash omega$ and $\backslash vec\; v$ are the angular and linear velocity vectors at the point $\backslash vec\; x$, respectively; $\backslash tilde\; I$ is the moment of inertia tensor, $m$ is the body's mass; $\backslash hat\; n$ is a unit normal to the surface of the body at the point $\backslash vec\; x$; $p$ is a pressure at this point; $\backslash vec\; Q\_h$ and $\backslash vec\; F\_h$ are the hydrodynamic torque and force acting on the body, respectively; $\backslash vec\; Q$ and $\backslash vec\; F$ likewise denote all other torques and forces acting on the body. The integration is performed over the fluid-exposed portion of the body's surface. If the body is completely submerged body in an infinitely large volume of irrotational, incompressible, inviscid fluid, that is at rest at infinity, then the vectors $\backslash vec\; Q\_h$ and $\backslash vec\; F\_h$ can be found via explicit integration, and the dynamics of the body is described by the Kirchhoff – Clebsch equations: : $$ } = \times \vec \omega, : $$ L(\vec \omega, \vec v) = (A \vec \omega,\vec \omega) + (B \vec \omega,\vec v) + (C \vec v,\vec v) + (\vec k,\vec \omega) + (\vec l,\vec v). Their first integrals read : $$ J_0 = \left(, \vec \omega \right) + \left(, \vec v \right) - L, \quad J_1 = \left(,\right), \quad J_2 = \left(,\right) . Further integration produces explicit expressions for position and velocities. == References == * Kirchhoff G. R. ''Vorlesungen ueber Mathematische Physik, Mechanik''. Lecture 19. Leipzig: Teubner. 1877. * Lamb, H., ''Hydrodynamics''. Sixth Edition Cambridge (UK): Cambridge University Press. 1932. 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「Kirchhoff equations」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.