Active and passive transformation: Difference between revisions

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[[File:PassiveActive.JPG|thumb|310px|In the active transformation (left), a point moves from position P to P' by rotating clockwise by an angle θ about the origin of the coordinate system. In the passive transformation (right), point P does not move, while the coordinate system rotates counterclockwise by an angle θ about its origin. The coordinates of P' in the active case (i.e. relative to the original coordinate system) are the same as the coordinates of P relative to the rotated coordinate system.]]
 
In [[physics]] and [[engineering]], an '''active transformation''', or '''alibi transformation'''<ref>[http://mathworld.wolfram.com/AlibiTransformation.html Weisstein, Eric W. "Alibi Transformation." From MathWorld--A Wolfram Web Resource.]</ref>, is a [[Transformation (mathematics)|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'''<ref>[http://mathworld.wolfram.com/AliasTransformation.html Weisstein, Eric W. "Alias Transformation." From MathWorld--A Wolfram Web Resource.]</ref>, 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'', [[mathematician]]s usually refer to active transformations, while [[physicist]]s and [[engineer]]s could mean either.
 
Put differently, a ''passive'' transformation refers to description of the ''same'' object in two different coordinate systems.<ref name= Davidson>
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