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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 Udwadia–Kalaba equation ： ウィキペディア英語版 Udwadia–Kalaba equation In theoretical physics, the Udwadia–Kalaba equation 〔Udwadia, F.E.; Kalaba, R.E. (1996). ''Analytical Dynamics: A New Approach.'' Cambridge University Press. ISBN 0-521-04833-8〕 is a method for deriving the equations of motion of a constrained mechanical system. This equation was discovered by Firdaus E. Udwadia and Robert E. Kalaba in 1992. The fundamental equation is the simplest and most comprehensive equation so far discovered for writing down the equations of motion of a constrained mechanical system. Although it is mostly a restatement of Newton's second law of motion, it makes a convenient distinction between externally applied forces and the internal forces of constraint, similar to the use of constraints in Lagrangian mechanics, but without the use of Lagrange multipliers. The Udwadia–Kalaba equation applies to a wide class of constraints, both holonomic constraints and nonholonomic ones, as long as they are linear with respect to the accelerations. The equation even generalizes to constraint forces that do not obey D'Alembert's principle. == The central problem of constrained motion == In the study of the dynamics of mechanical systems, the configuration of a given system ''S'' is, in general, completely described by ''n'' generalized coordinates so that its generalized coordinate ''n''-vector is given by :$\backslash mathbf:=()^\backslash mathrm.$ where T denotes matrix transpose. Using Newtonian or Lagrangian dynamics, the unconstrained equations of motion of the system ''S'' under study can be derived as a matrix equation (see matrix multiplication): (t)=\mathbf(q,\dot,t)\,, |cellpadding = 6 |border = 1 |border colour = black |background colour=white}} where the dots represent derivatives with respect to time: :$\backslash dot\_i\; =\; \backslash frac\backslash ,.$ It is assumed that the initial conditions q(0) and $\backslash dot\}(0)$ may be arbitrarily assigned. The ''n''-vector Q denotes the total generalized force acted on the system by some external influence; it can be expressed as the sum of all the conservative forces as well as ''non''-conservative forces. The ''n''-by-''n'' matrix M is symmetric, and it can be positive definite $(\backslash mathbf\; >\; 0)$ or semi-positive definite $(\backslash mathbf\; \backslash geq\; 0)$. Typically, it is assumed that M is positive definite; however, it is not uncommon to derive the unconstrained equations of motion of the system ''S'' such that M is only semi-positive definite; i.e., the mass matrix may be singular (it has no inverse matrix). 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「Udwadia–Kalaba equation」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.