翻訳と辞書 Words near each other ・ Lissa Labiche ・ Lissa Lauria ・ Lissa Muscatine ・ Lissa Vera ・ Lissa'aere ・ Lissac ・ Lissac, Ariège ・ Lissac, Haute-Loire ・ Lissac-et-Mouret ・ Lissac-sur-Couze ・ Lissadell ・ Lissadell House ・ Lissagurraun ・ Lissajous ・ Lissajous curve ・ Lissajous knot ・ Lissajous orbit ・ Lissamphibia ・ Lissan ・ Lissan GAC ・ Lissan House ・ Lissanthe ・ Lissanthe sapida ・ Lissanthe strigosa ・ Lissauer ・ Lissauer Breccia ・ Lissavruggy ・ Lissay-Lochy ・ Lissazounmè ・ Lisse 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 Lissajous knot ： ウィキペディア英語版 Lissajous knot In knot theory, a Lissajous knot is a knot defined by parametric equations of the form :$x\; =\; \backslash cos(n\_x\; t\; +\; \backslash phi\_x),\backslash qquad\; y\; =\; \backslash cos(n\_y\; t\; +\; \backslash phi\_y),\; \backslash qquad\; z\; =\; \backslash cos(n\_z\; t\; +\; \backslash phi\_z),$ where $n\_x$, $n\_y$, and $n\_z$ are integers and the phase shifts $\backslash phi\_x$, $\backslash phi\_y$, and $\backslash phi\_z$ may be any real numbers.〔M.G.V. Bogle, J.E. Hearst, V.F.R. Jones, L. Stoilov, "Lissajous knots", Journal of Knot Theory and Its Ramifications, 3(2), 1994, 121–140.〕 The projection of a Lissajous knot onto any of the three coordinate planes is a Lissajous curve, and many of the properties of these knots are closely related to properties of Lissajous curves. Replacing the cosine function in the parametrization by a triangle wave transforms every Lissajous knot isotopically into a billiard curve inside a cube, the simplest case of so-called ''billiard knots''. Billiard knots can also be studied in other domains, for instance in a cylinder.〔C. Lamm, D. Obermeyer. "Billiard knots in a cylinder", Journal of Knot Theory and Its Ramifications, 8(3), 1999, 353–366.〕 == Form == Because a knot cannot be self-intersecting, the three integers $n\_x,\; n\_y,\; n\_z$ must be pairwise relatively prime, and none of the quantities :$n\_x\; \backslash phi\_y\; -\; n\_y\; \backslash phi\_x,\backslash quad\; n\_y\; \backslash phi\_z\; -\; n\_z\; \backslash phi\_y,\backslash quad\; n\_z\; \backslash phi\_x\; -\; n\_x\; \backslash phi\_z$ may be an integer multiple of pi. Moreover, by making a substitution of the form $t\text{'}\; =\; t+c$, one may assume that any of the three phase shifts $\backslash phi\_x$, $\backslash phi\_y$, $\backslash phi\_z$ is equal to zero. 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「Lissajous knot」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.