翻訳と辞書 Words near each other ・ Bonnie Bell, California ・ Bonnie Berger ・ Bonnie Bergin ・ Bonnie Bernstein ・ Bonnie Bishop ・ Bonnie Blair ・ Bonnie Blue Flag ・ Bonnie Bluh ・ Bonnie Bo ・ Bonnie Bonnell ・ Bonnie Bonnie Lassie ・ Bonnie Bowman ・ Bonnie Bracey ・ Bonnie Bramlett ・ Bonnie Brinton ・ Bonnet's theorem ・ Bonnet, Meuse ・ Bonnetan ・ Bonneterre Formation ・ Bonneterrina ・ Bonnethead ・ Bonnetia ・ Bonnetia bolivarensis ・ Bonnetia celiae ・ Bonnetia chimantensis ・ Bonnetia cordifolia ・ Bonnetia fasciculata ・ Bonnetia holostyla ・ Bonnetia jauaensis ・ Bonnetia kathleenae 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 Bonnet's theorem ： ウィキペディア英語版 Bonnet's theorem In classical mechanics, Bonnet's theorem states that if ''n'' different force fields each produce the same geometric orbit (say, an ellipse of given dimensions) albeit with different speeds ''v''1, ''v''2,...,''v''''n'' at a given point ''P'', then the same orbit will be followed if the speed at point ''P'' equals :$$ v_^ + v_^ + \cdots + v_^} This theorem was first derived by Adrien-Marie Legendre in 1817, but it is named after Pierre Ossian Bonnet. ==Derivation== The shape of an orbit is determined only by the centripetal forces at each point of the orbit, which are the forces acting perpendicular to the orbit. By contrast, forces ''along'' the orbit change only the speed, but not the direction, of the velocity. Let the instantaneous radius of curvature at a point ''P'' on the orbit be denoted as ''R''. For the ''k''th force field that produces that orbit, the force normal to the orbit ''F''''k'' must provide the centripetal force :$$ F_ = \frac v_^ Adding all these forces together yields the equation :$$ \sum_^ F_ = \frac \sum_^ v_^ Hence, the combined force-field produces the same orbit if the speed at a point ''P'' is set equal to :$$ v_^ + v_^ + \cdots + v_^} 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「Bonnet'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.