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Would there be a book that does what Landau does in Fluid Mechanics and Theory of Elasticity using Lagrangian's/Action-principles, analogous to the presentation in Landau's mechanics?

I have only found brief mentions of a Lagrangian in Fluid mechanics, e.g. Stone and Lanczos, and nothing useful for elasticity.

Would sincerely appreciate a reference, thanks.

References:

  1. Stone - Mathematics for Physics: A Guided Tour for Graduate Students, p. 25.
  2. Lanczos - The Variational Principles of Mechanics, p. 360.
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  • $\begingroup$ Did you try to Google? $\endgroup$
    – Qmechanic
    Jul 23, 2014 at 14:00

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You should check out Marsden and Hughes's Mathematical Foundations of Elasticity.

It is a book that requires a lot of work (I am going through it myself and it is not easy!), using the very general framework of tensors on manifolds and functional analysis, but it is an invaluable resource.

Two chapters in that book (5. Hamiltonian And Variational Principles and 6. Methods Of Functional Analysis In Elasticity) are particularly relevant to your question.

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  • $\begingroup$ Thanks very much, but I've tried many times to relate Marsden Ch. 5 to Landau and can't do it. $\endgroup$
    – bolbteppa
    Jul 23, 2014 at 15:06
  • $\begingroup$ @bolbteppa Are you interested in the infinitesimal theory or finite strain theory? $\endgroup$ Jul 23, 2014 at 15:33
  • $\begingroup$ I don't really know unfortunately, I'm more just hoping there is an exposition that starts with an action, derives a few general Lagrangians, derives all the tensors, Euler, Bernoulli, Cauchy etc... via Noether's theorem, then works some problems. Have you come across anything like that? $\endgroup$
    – bolbteppa
    Jul 23, 2014 at 15:57
  • $\begingroup$ Well, I asked because for infinitesimal (linearized) elasticity you can find the lagrangian in this answer physics.stackexchange.com/q/2808 Note that it is still of the form L = T - U. $\endgroup$ Jul 23, 2014 at 16:06

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