Action Principles in Continuum Mechanics?

bolbteppa
Messages
300
Reaction score
41
Is there any book that does what Landau does in Fluid Mechanics and Theory of Elasticity, only using a Lagrangian/Action-principles the whole way through?

I can really only find brief tiny descriptions like this one in books on other topics, is there nothing that does for fluids/elasticity like what Landau does for mechanics and em?
 
Physics news on Phys.org
I'm sorry you are not finding help at the moment. Is there any additional information you can share with us?
 
The only source I know is

A. Sommerfeld, Lectures on Theoretical Physics

It's anyway a marvelous theoretical-physics book series (6 volumes). Particularly vol. 6 about partial differential equations is great.

I once worked this out for myself for a student seminar on hydrodynamics. Unfortunately I have this only in German. Perhaps even this helps a bit, because there are many formulae.

http://theory.gsi.de/~vanhees/faq/hydro/hydro.html
http://theory.gsi.de/~vanhees/faq-pdf/hydro.pdf
 
I'm very appreciative of your notes, thank you. I will use google translate to refer to them when I sit down to do this properly. I looked in Sommerfeld and from memory found Lanczos gives a better presentation of the same material, but I'll check it again.

Regarding fluid mechanics, my main concern is that one apparently it's been proven that can't derive Navier-Stokes or any viscous fluid dynamics from an action principle (i.e. friction, a velocity dependent potential), so at best we can do chapter 1 of Landau via action principles + Noether's theorem and no more... However this book

www.amazon.com/Hamilton-Type-Principle-Fluid-Dynamics-Magnetohydrodynamics/dp/3211249648/[/URL]

claims to do it, and apparently explains the flaw in the old approach, page 16 - 17:

[url]http://books.google.ie/books?id=ONGsaXO1VToC&lpg=PA18&ots=3Le8YeDRaS&dq=Angel%20Fierros%20Palacios&pg=PA16#v=onepage&q=Angel%20Fierros%20Palacios&f=false[/url]

While it might be cranky, the only review I can find

[url]http://onlinelibrary.wiley.com/doi/10.1002/andp.200610224/abstract[/url]

gives the book a bad review but doesn't even mention this important issue, it gives out about the book for absolutely ridiculous reasons tbh so it's not a credible source.

The other approach is differential forms, which apparently can derive Navier-Stokes nice enough, just have to find a nice presentation.

Anybody have any thoughts on these, it's be great to read them.
 
Last edited by a moderator:

Similar threads

  • · Replies 2 ·
Replies
2
Views
2K
Replies
28
Views
6K
  • · Replies 7 ·
Replies
7
Views
10K
  • · Replies 8 ·
Replies
8
Views
4K
  • · Replies 9 ·
Replies
9
Views
1K
  • · Replies 23 ·
Replies
23
Views
8K
  • · Replies 14 ·
Replies
14
Views
3K
  • · Replies 19 ·
Replies
19
Views
7K
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 3 ·
Replies
3
Views
4K