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Lie Derivative, Deformation Rate, Velocity Gradient

Submitted by John Craighead on

I'm trying to understand elastic deformation using the Lie derivative. I've read a good summary on Wiki but want other sources to review. Can anyone offer any sources &/or explanations. I need something fairly basic. Thanks, John.

Andras Nelhiebel

Hello John,

I have recently seen your blog, and I would like to respond.

I think Lie derivative is not an easy topic at all, so I think there is no simple explanation (or the simple explanation is not exhaustive).

My suggestion would be to look at Frankel: The Geometry of Physics, for the mathematical background, and then Marsden-Hughes: Mathematical Foundations of Elasticity for the role of Lie derivative in elasticity.

I know that they are a bit advanced, but the insight thees books give is worth it.

Andras

Tue, 08/17/2010 - 21:04 Permalink
John Craighead

Andras,

Thanks very much for suggesting the books & also kind words about Lie derivative being challenging. I have been using Marsden/Hughes &, with some time, have begun to understand (some of) it. I'll try Frankel. 

In the meantime, I have found some lecture notes from Prof. Pandolfi at Milano Tech. which have been a good starting point. Also, some papers on geometric kinematics by Marsden, Hughes et al. If any of this of interest, I'm pleased to share.

 Thanks, John. 

Tue, 08/31/2010 - 12:52 Permalink
George Papazaf…

John take a look at these links:

1) 3 papers related to elasticity and Lie derivative 

http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6VJS-482GP1M-5T&_user=83473&_coverDate=12%2F31%2F1993&_rdoc=1&_fmt=high&_orig=search&_sort=d&_docanchor=&view=c&_searchStrId=1434903127&_rerunOrigin=google&_acct=C000059671&_version=1&_urlVersion=0&_userid=83473&md5=58122dfcbccfddeeea776d9909e5fb5c

http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6X42-4FPHTWY-14&_user=83473&_coverDate=12%2F31%2F1956&_rdoc=1&_fmt=high&_orig=search&_sort=d&_docanchor=&view=c&_searchStrId=1434903287&_rerunOrigin=google&_acct=C000059671&_version=1&_urlVersion=0&_userid=83473&md5=5d7720d6fee667d3af573440a64754a9

http://onlinelibrary.wiley.com/doi/10.1002/nme.1620290304/pdf

b) 3 books:

http://www.emis.de/monographs/KSM/kmsbookh.pdf

http://openlibrary.org/books/OL3427193M/Gauge_theory_and_variational_principles

http://www.scribd.com/doc/18077688/Foundations-of-Mechanics

I hope I helped you.

Best regards,

 

George Papazafeiropoulos

________________________

Second Lieutenant, Hellenic Air Force

Civil Engineer (M.Sc), Ph.D. Candidate

Wed, 08/18/2010 - 22:09 Permalink
George Papazaf…

Dear John,

 Unfortunately I don't remember the details of the paper you want. When I have time I will re-search for it in scholar.google. Wait a little because I have a lot of work to do these days ok?

 Best regards,

 

George Papazafeiropoulos

________________________

Second Lieutenant, Hellenic Air Force

Civil Engineer (M.Sc), Ph.D. Candidate

Thu, 09/02/2010 - 18:50 Permalink