翻訳と辞書 Words near each other ・ Geometric graph theory ・ Geometric group action ・ Geometric group theory ・ Geometric hashing ・ Geometric integration ・ Geometric integrator ・ Geometric invariant theory ・ Geometric Langlands correspondence ・ Geometric lathe ・ Geometric lattice ・ Geometric magic square ・ Geometric mean ・ Geometric mean theorem ・ Geometric measure of entanglement ・ Geometric measure theory ・ Geometric mechanics ・ Geometric median ・ Geometric modeling ・ Geometric modeling kernel ・ Geometric moray ・ Geometric Morphometrics in Anthropology ・ Geometric Mouse, Variation I, Scale A ・ Geometric networks ・ Geometric phase ・ Geometric phase analysis ・ Geometric Poisson distribution ・ Geometric primitive ・ Geometric probability ・ Geometric programming ・ Geometric progression 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 Geometric mechanics ： ウィキペディア英語版 Geometric mechanics Geometric mechanics is a branch of mathematics applying particular geometric methods to many areas of mechanics, from mechanics of particles and rigid bodies to fluid mechanics to control theory. Geometric mechanics applies principally to systems for which the configuration space is a Lie group, or a group of diffeomorphisms, or more generally where some aspect of the configuration space has this group structure. For example, the configuration space of a rigid body such as a satellite is the group of Euclidean motions (translations and rotations in space), while the configuration space for a liquid crystal is the group of diffeomorphisms coupled with an internal state (gauge symmetry or order parameter). == Momentum map and reduction == One of the principal ideas of Geometric Mechanics is ''reduction'', which goes back to Jacobi's elimination of the node in the 3-body problem, but in its modern form is due to K. Meyer (1973) and independently J.E. Marsden and A. Weinstein (1974), both inspired by the work of Smale (1970). Symmetry of a Hamiltonian or Lagrangian system gives rise to conserved quantities, by Noether's theorem, and these conserved quantities are the components of the momentum map J. If ''P'' is the phase space and ''G'' the symmetry group, the momentum map is a map $\backslash mathbf:P\backslash to\backslash mathfrak^$ *, and the reduced spaces are quotients of the level sets of J by the subgroup of ''G'' preserving the level set in question: for $\backslash mu\backslash in\backslash mathfrak^$ * one defines $P\_\backslash mu=\backslash mathbf^(\backslash mu)/G\_\backslash mu$, and this reduced space is a symplectic manifold if $\backslash mu$ is a regular value of ''J''. 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「Geometric mechanics」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.