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In physics, a Galilean transformation is used to transform between the coordinates of two reference frames which differ only by constant relative motion within the constructs of Newtonian physics, and forms the Galilean group. It is the group of motions of Galilean relativity action on the four dimensions of space and time, forming the Galilean geometry. This is the passive transformation point of view. The equations below, although apparently obvious, are valid only at speeds much less than the speed of light. In special relativity the Galilean transformations are replaced by Poincaré transformations; conversely, the group contraction in the classical limit of Poincaré transformations yields Galilean transformations. Galileo formulated these concepts in his description of ''uniform motion''.〔Galileo 1638 ''Discorsi e Dimostrazioni Matematiche, intorno á due nuoue scienze'' 191–196, published by Lowys Elzevir (Louis Elsevier), Leiden, or ''Two New Sciences'', English translation by Henry Crew and Alfonso de Salvio 1914, reprinted on pages 515–520 of ''On the Shoulders of Giants'': The Great Works of Physics and Astronomy. Stephen Hawking, ed. 2002 ISBN 0-7624-1348-4〕 The topic was motivated by Galileo's description of the motion of a ball rolling down a ramp, by which he measured the numerical value for the acceleration of gravity near the surface of the Earth. ==Translation== Though the transformations are named for Galileo, it is absolute time and space as conceived by Isaac Newton that provides their domain of definition. In essence, the Galilean transformations embody the intuitive notion of addition and subtraction of velocities as vectors. This assumption is abandoned in the Poincaré transformations. These relativistic transformations are applicable to all velocities, whilst the Galilean transformation can be regarded as a low-velocity approximation to the Poincaré transformation. The notation below describes the relationship under the Galilean transformation between the coordinates and of a single arbitrary event, as measured in two coordinate systems S and S', in uniform relative motion (velocity ''v'') in their common ''x'' and ''x''′ directions, with their spatial origins coinciding at time : 〔, (Chapter 2 §2.6, p. 42 )〕 〔, (Chapter 38 §38.2, p. 1046,1047 )〕 〔, (Chapter 9 §9.1, p. 261 )〕 〔, (Chapter 5, p. 83 )〕 : : : : Note that the last equation expresses the assumption of a universal time independent of the relative motion of different observers. In the language of linear algebra, this transformation is considered a shear mapping, and is described with a matrix acting on a vector. With motion parallel to the ''x''-axis, the transformation acts on only two components: : Though matrix representations are not strictly necessary for Galilean transformation, they provide the means for direct comparison to transformation methods in special relativity. 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「Galilean transformation」の詳細全文を読む スポンサード リンク
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