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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 Rigid body dynamics ： ウィキペディア英語版 Rigid body dynamics Rigid-body dynamics studies the movement of systems of interconnected bodies under the action of external forces. The assumption that the bodies are rigid, which means that they do not deform under the action of applied forces, simplifies the analysis by reducing the parameters that describe the configuration of the system to the translation and rotation of reference frames attached to each body.〔B. Paul, Kinematics and Dynamics of Planar Machinery, Prentice-Hall, NJ, 1979〕〔L. W. Tsai, Robot Analysis: The mechanics of serial and parallel manipulators, John-Wiley, NY, 1999.〕 The dynamics of a rigid body system is defined by its equations of motion, which are derived using either Newtons laws of motion or Lagrangian mechanics. The solution of these equations of motion defines how the configuration of the system of rigid bodies changes as a function of time. The formulation and solution of rigid body dynamics is an important tool in the computer simulation of mechanical systems. ==Planar rigid body dynamics== If a rigid system of particles moves such that the trajectory of every particle is parallel to a fixed plane, the system is said to be constrained to planar movement. In this case, Newton's laws for a rigid system of N particles, P, i=1,...,N, simplify because there is no movement in the ''k'' direction. Determine the resultant force and torque at a reference point R, to obtain :$\backslash mathbf\; =\; \backslash sum\_^N\; m\_i\backslash mathbf\_i,\backslash quad\; \backslash mathbf\; =\; \backslash sum\_^N\; (\backslash mathbf\_i-\backslash mathbf)\backslash times\; (m\_i\backslash mathbf\_i),$ where r denotes the planar trajectory of each particle. The kinematics of a rigid body yields the formula for the acceleration of the particle P in terms of the position R and acceleration A of the reference particle as well as the angular velocity vector ω and angular acceleration vector α of the rigid system of particles as, :$\backslash mathbf\_i\; =\; \backslash alpha\backslash times(\backslash mathbf\_i-\backslash mathbf)\; +\; \backslash omega\backslash times\backslash omega\backslash times(\backslash mathbf\_i-\backslash mathbf)\; +\; \backslash mathbf.$ For systems that are constrained to planar movement, the angular velocity and angular acceleration vectors are directed along ''k'' perpendicular to the plane of movement, which simplifies this acceleration equation. In this case, the acceleration vectors can be simplified by introducing the unit vectors e from the reference point R to a point r and the unit vectors t=''k''xe, so :$\backslash mathbf\_i\; =\; \backslash alpha(\backslash Delta\; r\_i\backslash mathbf\_)\; -\; \backslash omega^2(\backslash Delta\; r\_i\backslash mathbf\_)\; +\; \backslash mathbf.$ This yields the resultant force on the system as :$\backslash mathbf\; =\; \backslash alpha\backslash sum\_^N\; m\_i\; (\backslash Delta\; r\_i\backslash mathbf\_)\; -\; \backslash omega^2\backslash sum\_^N\; m\_i\; (\backslash Delta\; r\_i\backslash mathbf\_)\; +\; (\backslash sum\_^N\; m\_i)\backslash mathbf,$ and torque as :$\backslash mathbf\; =\backslash sum\_^N\; (m\_i\backslash Delta\; r\_i\backslash mathbf\_i)\backslash times\; (\backslash alpha(\backslash Delta\; r\_i\backslash mathbf\_)\; -\; \backslash omega^2(\backslash Delta\; r\_i\backslash mathbf\_)\; +\; \backslash mathbf)\; =\; (\backslash sum\_^N\; m\_i\backslash Delta\; r\_i^2)\backslash alpha\backslash vec\; +\; (\backslash sum\_^N\; m\_i\backslash Delta\; r\_i\backslash mathbf\_i)\backslash times\backslash mathbf,$ where exe=0, and ext=''k'' is the unit vector perpendicular to the plane for all of the particles P. Use the center of mass C as the reference point, so these equations for Newton's laws simplify to become :$\backslash mathbf\; =\; M\backslash mathbf,\backslash quad\; \backslash mathbf\; =\; I\_C\backslash alpha\backslash vec,$ where M is the total mass and I is the moment of inertia about an axis perpendicular to the movement of the rigid system and through the center of mass. 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「Rigid body dynamics」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.