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In physics and engineering, an active transformation, or alibi transformation, is a transformation which actually changes the physical position of a point, or rigid body, which can be defined even in the absence of a coordinate system; whereas a passive transformation, or alias transformation, is merely a change in the coordinate system in which the object is described (change of coordinate map, or change of basis). By default, by ''transformation'', mathematicians usually refer to active transformations, while physicists and engineers could mean either. Put differently, a ''passive'' transformation refers to description of the ''same'' object in two different coordinate systems.〔 〕 On the other hand, an ''active transformation'' is a transformation of one or more objects with respect to the same coordinate system. For instance, active transformations are useful to describe successive positions of a rigid body. On the other hand, passive transformations may be useful in human motion analysis to observe the motion of the tibia relative to the femur, i.e. its motion relative to a (''local'') coordinate system which moves together with the femur, rather than a (''global'') coordinate system which is fixed to the floor.〔 == Example == As an example, in the vector space ℝ2, let be a basis, and consider the vector v = ''v''1e1 + ''v''2e2. A rotation of the vector through angle θ is given by the matrix: : which can be viewed either as an active transformation or a passive transformation (where the matrix is inverse), as described below. 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「Active and passive transformation」の詳細全文を読む スポンサード リンク
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