Difference between revisions of "Realization of transformations"
From Robotics
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q' = e\ q\ e^*+ p | q' = e\ q\ e^*+ p | ||
</math> | </math> | ||
+ | |||
+ | ===Combination of transformations=== | ||
It is known that a [[Combinations of transformations|combination of transformations]] is defined as: | It is known that a [[Combinations of transformations|combination of transformations]] is defined as: |
Revision as of 16:02, 15 October 2015
← Back: Composition of rotations | Overview: Quaternions | Next: ??? → |
Up to now transformations have been defined by homogeneous matrices combining a rotation matrix and a translation vector
. Now a new notation is introduced to represent a transformation using two quaternions
and
:
The quaternion is equivalent to
and describes the rotation while
is defined as
and so equivalent to the translation.
Applying such a transformation to a quaternion is done by first rotating
with
corresponding to the rotation equation and then adding
:
Combination of transformations
It is known that a combination of transformations is defined as: