翻訳と辞書 Words near each other ・ Sia Partners ・ Sia Saran ・ Sia Saran-e Olya ・ Sia Saran-e Sofla ・ SIA Scotch Whisky ・ Sia Sia ・ Sia Sia-ye Keykhosrow ・ Sia Wai Yen ・ Sia, Cyprus ・ Sia, le rêve du python ・ SIAA ・ Siab ・ Siab-e Darvish ・ Siabkun ・ SIAC ・ Siacci's theorem ・ Siachen Base Camp (India) ・ Siachen conflict ・ Siachen Glacier ・ Siachen Glacier Medal ・ Siachen Muztagh ・ Siachoque ・ Siad Barre ・ Siadabida Manda ・ Siadak ・ Siadak Deh Mardeh ・ Siadak, Hirmand ・ Siadar Wave Power Station ・ Siadcza, Lubusz Voivodeship ・ Siadcza, Silesian Voivodeship Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Siacci's theorem ： ウィキペディア英語版 Siacci's theorem In kinematics, the acceleration of a particle moving along a curve in space is the time derivative of its velocity. In most applications, the acceleration vector is expressed as the sum of its normal and tangential components, which are orthogonal to each other. Siacci’s theorem, formulated by the Italian mathematician Francesco Siacci (1839–1907), is the kinematical decomposition of the acceleration vector into its radial and tangential components. In general, the radial and tangential components are not orthogonal to each other. Siacci’s theorem is particularly useful in motions where the angular momentum is constant. ==Siacci's theorem in the plane== Let a particle ''P'' of mass ''m''  move in a two-dimensional Euclidean space (planar motion). Suppose that ''C'' is the curve traced out by ''P'' and ''s'' is the arc length of ''C'' corresponding to time ''t''. Let ''O'' be an arbitrary origin in the plane and be a fixed orthonormal basis. The position vector of the particle is :$\backslash mathbf\; =\; r\; \backslash mathbf\_r\; .$ The unit vector er is the radial basis vector of a polar coordinate system in the plane. The velocity vector of the particle is :$\backslash mathbf\; =\; \backslash frac\; =\; \backslash dot\backslash mathbf\_t\; =\; v\backslash mathbf\_t\; ,$ where e''t'' is the unit tangent vector to ''C''. Define the angular momentum of ''P'' as :$\backslash mathbf\; =\; \backslash mathbf\; \backslash times\; m\backslash mathbf\; =\; h\backslash mathbf,$ where k = i x j. Assume that ''h ≠ 0''. The position vector r may then be expressed as :$\backslash mathbf\; =\; q\backslash mathbf\_t\; -\; p\backslash mathbf\_n$ in the Serret-Frenet Basis . The magnitude of the angular momentum is ''h'' = ''mpv'', where ''p'' is the perpendicular from the origin to the tangent line ''ZP''. According to Siacci’s theorem, the acceleration a of ''P'' can be expressed as :$\backslash mathbf\; =\; -\backslash frac\; \backslash mathbf\_r\; +\; \backslash frac\; \backslash mathbf\_t\; =\; S\_r\; \backslash mathbf\_r\; +\; S\_t\; \backslash mathbf\_t\; .$ where the prime denotes differentiation with respect to the arc length ''s'', and ''κ'' is the curvature function of the curve ''C''. In general, ''Sr'' and ''St'' are not equal to the orthogonal projections of a onto er and et. 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「Siacci's theorem」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.