![]() ![]() ![]() Three unit vectors of frame G described in frame L ( ), the following orthogonality Unit vectors of frame L described in frame G and the columns are the Using, one can easily form the transformation matricesįrom the global frame to the local frames. Of the markers is a relatively simple task if the local reference frames are well-defined. This exercise is quite useful since the immediate products of motionĪnalysis is the global coordinates of the markers attached to the subject's body andĬomputation of the unit vectors of the local reference frames from the global coordinates In frame G, while the second and third rows are the same to unit vectors j'Īnd k' described in frame G, respectively. Therefore, theįirst row of the transformation matrix becomes the same to i' described Vectors of the two reference frames are in fact the same to the components of i', Transformation matrix of T L/G, can also beĪs shown in and, T G/L is in fact the same To a particular local reference frame (frame L) can be written as Transformation matrix from the global reference frame (frame G) & k' = the unit vectors of the X'Y'Z' system. ![]() = the unit vectors of the XYZ system, and i', j' A transformation alters not the vector, but the To transform a vector from one reference frame to another isĮquivalent to changing the perspective of describing the vector from one to another ( Figure 1).
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