Active and passive transformation: Difference between revisions

no edit summary
 
[[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''', is a [[Transformation (mathematics)|transformation]] which actually changes the physical position of a point, or [[rigid body]], 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.
 
In [[physics]] and [[engineering]], an '''active transformation''', or '''alibi transformation''', is a [[Transformation (mathematics)|transformation]] which actually changes the physical position of a point, or [[rigid body]], andwhich can makesbe sensedefined even in the absence of a [[coordinate system]]; whereas a '''passive transformation''', or '''alias transformation''', is merely a change in the position of the coordinate system fromin which the object is observeddescribed (change of coordinate map, or [[change of basis]]). By default, by ''transformation'', [[mathematician]]s usually meanrefer to 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>
 
Put differently, a ''passive'' transformation refers to observationdescription of the ''same'' eventobject fromin two different coordinate systems.<ref name= Davidson>
{{cite book |title=Robots and screw theory: applications of kinematics and statics to robotics
|author=Joseph K. Davidson, Kenneth Henderson Hunt
|isbn=0-19-856245-4 |year=2004 |publisher=Oxford University Press}}
</ref>
On the other hand, the ''active transformation'' is a new positiontransformation of allone pointsor more objects, relativewith respect to the same coordinate system. For instance, the active transformation is useful to describe successive positions of a [[rigid body]]. On the other hand, the passive transformation 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.<ref name = Davidson/>
 
== Example ==