Timeline for Velocity field of fluid and Maurer-Cartan form?
Current License: CC BY-SA 3.0
7 events
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| Jan 11, 2012 at 21:40 | comment | added | Qfwfq | Also, looking at page 15 of the same book, it seems that my $\dot{A}\cdot A^{-1}$ is, in the case of a flow $\varphi:\mathbb{R}\to G=\mathrm{SO}(3)$, what they call "spatial angular velocity", which lives in the Lie algebra of $G$. In the case of a flow of (volume preserving) diffeomorphisms it might be linked to the velocity field $v(t,x)$... | |
| Jan 11, 2012 at 21:01 | comment | added | Qfwfq | Thanks for the suggestion. I found in Arnold, Khezin Topological Methods in Hydrondynamics that 'my' definition was indeed the correct one; so question 1 is answered. | |
| Jan 11, 2012 at 20:09 | comment | added | Robert Bryant | This point of view has been discussed in the literature. You might, for example, look at Arnol'd's remarks about treating fluid flow as dynamics in the group of (volume preserving) diffeomorphisms in his "Mathematical Methods of Classical Mechanics" and the references that he cites there. | |
| Jan 11, 2012 at 19:56 | history | edited | Qfwfq | CC BY-SA 3.0 |
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| Jan 11, 2012 at 19:47 | history | edited | Qfwfq | CC BY-SA 3.0 |
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| Jan 11, 2012 at 19:03 | history | edited | Qfwfq | CC BY-SA 3.0 |
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| Jan 11, 2012 at 18:57 | history | asked | Qfwfq | CC BY-SA 3.0 |