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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 Jeans equations ： ウィキペディア英語版 Jeans equations The Jeans equations describe the motion of a collection of stars in a gravitational field. If ''n'' = ''n''(''x'',''t'') is the density of stars in space, as a function of position ''x'' = (''x''1, ''x''2, ''x''3) and time ''t'', ''v'' = (''v''1, ''v''2, ''v''3) is the velocity, and Φ = Φ(''x'',''t'') is the gravitational potential, the Jeans equations may be written as〔pp. 195-197, §4.2, ''Galactic dynamics'', James Binney, Scott Tremaine, Princeton University Press, 1988, ISBN 0-691-08445-9.〕 $$ \frac + \sum_i \frac=0, $$ \frac + n \frac + \sum_i \frac= 0 \qquad (j=1, 2, 3.) Here, the <…> notation means an average at a given point and time (x,t), so that, for example, $\backslash langle\backslash rangle$ is the average of component 1 of the velocity of the stars at a given point and time. The second set of equations may alternately be written as $$ n \frac + \sum_i n \langle\rangle \frac} = -n \frac - \sum_i \frac \qquad (j=1, 2, 3.) where $\backslash sigma\_^2=\backslash langle\backslash rangle-\backslash langle\backslash rangle\; \backslash langle\backslash rangle$ measures the velocity dispersion in components ''i'' and ''j'' at a given point. The Jeans equations are analogous to the Euler equations for fluid flow and may be derived from the collisionless Boltzmann equation. They were originally derived by James Clerk Maxwell but were first applied to stellar dynamics by James Jeans.〔p. 82, "On the theory of star-streaming and the structure of the universe", J. H. Jeans, ''Monthly Notices of the Royal Astronomical Society'' 76 (December 1915), pp. 70-84, .〕 ==References== 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「Jeans 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.