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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, Euler and Kovalevskaya tops ： ウィキペディア英語版 Lagrange, Euler and Kovalevskaya tops In classical mechanics, the precession of a top under the influence of gravity is not, in general, an integrable problem. There are however three famous cases that are integrable, the Euler, the Lagrange and the Kovalevskaya top.〔Audin, M. Spinning Tops: A Course on Integrable Systems. New York: Cambridge University Press, 1996.〕 In addition to the energy, each of these tops involves three additional constants of motion that give rise to the integrability. The Euler top describes a free top without any particular symmetry, moving in the absence of any external torque. The Lagrange top is a symmetric top, in which the center of gravity lies on the symmetry axis. The Kovalevskaya top〔S. Kovalevskaya, Acta Math. 12 177–232 (1889)〕〔A. M. Perelemov, Teoret. Mat. Fiz., Volume 131, Number 2, Pages 197–205 (2002)〕 is special symmetric top with a unique ratio of the moments of inertia satisfy the relation $I\_1=I\_2=\; 2\; I\_3$, and in which the center of gravity is located in the plane perpendicular to the symmetry axis. ==Hamiltonian Formulation of Classical tops== A classical top〔Herbert Goldstein Charles P. Poole , John L. Safko, Classical Mechanics, (3rd Edition), Addison-Wesley (2002)〕 is defined by three principal axes, defined by the three orthogonal vectors $\backslash hat\}^2$ and $\backslash hat$ along the principal axes $(l\_1,\; l\_2,\; l\_3)=\; (\backslash vec\backslash cdot\; \backslash hat\; \backslash cdot\; \backslash hat\; \backslash cdot\; \backslash hat\; \}\backslash cdot\; \backslash hat\; \}\backslash cdot\; \backslash hat\; \}\backslash cdot\; \backslash hat\; =\; \backslash epsilon\_l\_c,\; \backslash \; \backslash \; =\; \backslash epsilon\_n\_c,\; \backslash \; \backslash \; =\; 0$ If the position of the center of mass is given by $\backslash vec\_\; =\; (a\; \backslash mathbf^1\; +\; b\; \backslash mathbf^2\; +\; c\backslash mathbf^3)$, then the Hamiltonian of a top is given by $$ H = \frac+\frac+\frac+ mg (a n_1 + bn_2 + cn_3), The equations of motion are then determined by $$ \dot_a = \, \dot_a = \ 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, Euler and Kovalevskaya tops」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.