Active and passive transformation: Difference between revisions

Also known as alibi and alias transformations
(Simplifying. Using "coordinate system" rather than "coordinate frame". The most usual expressions are "reference frame", "coordinate system", "basis". Coordinate frame is less frequently used.)
(Also known as alibi and alias transformations)
 
[[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 are the same as the coordinates of P relative to the rotated coordinate system.]]
In the [[physics|physical]] sciencesand [[engineering]], an '''active transformation''', or '''alibi transformation''', is a [[Transformation (mathematics)|transformation]] which actually changes the physical position of a point, body, or physical [[system]] (e.g. the componentsrigid of an [[enginebody]]), and makes sense even in the absence of a [[coordinate system]] whereas a '''passive transformation''', or '''alias transformation''', is a change in the position of the coordinate system from which the object is observed ([[change of basis]]). By default, by ''transformation'', [[mathematician]]s usually mean active transformations, while [[physicist]]s and [[engineer]]s could mean either.
 
Put differently, a ''passive'' transformation refers to observation of the ''same'' event from two different coordinate systems.<ref name= Davidson>