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Citation bot (talk | contribs) Alter: isbn. Add: chapter-url. Removed or converted URL. Some additions/deletions were actually parameter name changes. | You can use this bot yourself. Report bugs here. | Activated by Amigao | Category:Systems theory | via #UCB_Category |
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{{cite book |title=Robots and screw theory: applications of kinematics and statics to robotics
|author=Joseph K. Davidson, Kenneth Henderson Hunt
|chapter=§4.4.1 The active interpretation and the active transformation |page=74 ''ff'' |chapter-url=https://books.google.com/books?id=OQq67Tr7D0cC&pg=PA74
|isbn=0-19-856245-4 |year=2004 |publisher=Oxford University Press}}
</ref>
Line 37:
On the other hand, when one views <math>T</math> as a passive transformation, the initial vector <math>\mathbf{v}=(v_x,v_y,v_z)</math> is left unchanged, while the coordinate system and its basis vectors are transformed in the opposite direction, that is, with the inverse transformation <math>T^{-1}</math>.
<ref name=Amidror>
{{cite book |isbn=978-1-4020-5457-
|chapter-url=https://books.google.com/books?id=Z_QRomE5g3QC&pg=PT361 |chapter=Appendix D: Remark D.12 |page=346 }}
</ref> This gives a new coordinate system XYZ with basis vectors:
:<math>\mathbf{e}_X=T^{-1}(1,0,0),\ \mathbf{e}_Y=T^{-1}(0,1,0),\ \mathbf{e}_Z=T^{-1}(0,0,1)</math>
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