Timeline for Use Lie Sub-Groups of GL(3, R) for elastic deformation ?
Current License: CC BY-SA 2.5
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| Sep 29, 2010 at 14:47 | comment | added | John Craighead | Scott, Thanks for the insights & context. My initial post should have mentioned my interest as homogeneous elastic deformation (F depending only on time, not position). By "represented", I mean representing these deformations as some combination of (sub)groups with physical meaning (i.e. pure stretch, shear, etc.) like done with rigid body motion (i.e. SO(3) X R^3). Thanks, John. | |
| Sep 29, 2010 at 14:11 | comment | added | S. Carnahan♦ | I think the answer is that it depends on what you mean by "represented". Often there is a volume-conservation constraint, so you are stuck with the subgroup $SL_2(\mathbf{R})$. The decompositions you mention are well-known in the theory of Lie groups, e.g., $F=RU$ is called Iwasawa decomposition. I should note that shears may have negative entries off the diagonal. | |
| Sep 29, 2010 at 14:07 | history | edited | S. Carnahan♦ | CC BY-SA 2.5 |
Lots of minor adjustments
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| Sep 29, 2010 at 13:45 | history | asked | John Craighead | CC BY-SA 2.5 |