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[[File:PassiveActive.JPGthumb310pxIn 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 (that is, relative to the original coordinate system) are the same as the coordinates of P relative to the rotated coordinate system.]]
In [[physics]] and [[engineering]], spatial transformations in the 3dimensional Euclidian space <math>\R^3</math> are distinguished into '''active''' or '''alibi transformations''', and '''passive''' or '''alias transformstions'''. An '''active transformation'''<ref>[http://mathworld.wolfram.com/AlibiTransformation.html Weisstein, Eric W. "Alibi Transformation." From MathWorldA Wolfram Web Resource.]</ref> is a [[Transformation (mathematics)transformation]] which actually changes the physical position (alibi, elsewhere) of a point, or [[rigid body]], which can be defined
Put differently, a ''passive'' transformation refers to description of the ''same'' object in two different coordinate systems.<ref name= Davidson>
isbn=0198562454 year=2004 publisher=Oxford University Press}}
</ref>
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
== Example ==
