Which books are good for Lagrangian/Hamiltonian formulations for continuum?

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Discussion Overview

The discussion centers on recommendations for books that cover Lagrangian and Hamiltonian formulations in continuum mechanics. Participants seek resources that are accessible and provide a comprehensive treatment of the subject beyond commonly referenced texts.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • Some participants suggest "Classical Mechanics" by John R. Taylor as a good resource, although one participant notes it lacks a direct relation to Lagrangian/Hamiltonian formulations.
  • A. Sommerfeld's "Lectures on Theoretical Physics, vol. 2" is recommended for its sections on incompressible and compressible ideal fluids.
  • Participants mention Soper's "Classical Field Theory" as an elegant treatment for the relativistic case.
  • Florian Scheck's "Mechanics" is noted as a good introduction, but some participants feel that the coverage in various recommended texts is insufficient.
  • Marsden & Hughes' work on elasticity is mentioned as potentially useful, along with resources from Darryl Holm.
  • Several other titles are proposed, including "A Student's Guide to Lagrangian and Hamiltonians" by Hamill, "Lagrangian & Hamiltonian Dynamics" by Mann, and "Theoretical Mechanics of Particles and Continua" by Fetter & Walecka, though concerns about their depth are expressed.
  • Berdichevsky's two-volume monograph is highlighted as a detailed graduate-level text, though it is suggested that it may be challenging to follow.
  • Additional suggestions include works by Auria & Trigiante and Susskind, focusing on classical field theory and its applications.

Areas of Agreement / Disagreement

Participants express varying opinions on the accessibility and depth of the recommended texts, with no consensus on a single best resource. Some participants find certain books too complex, while others advocate for their value.

Contextual Notes

Participants note that many suggested books cover Lagrangian and Hamiltonian formulations in limited sections, which may not be sufficient for comprehensive understanding. There is also mention of the varying difficulty levels of the texts.

Who May Find This Useful

This discussion may be useful for students and researchers looking for accessible resources on Lagrangian and Hamiltonian formulations in continuum mechanics, particularly those seeking alternatives to more complex standard texts.

thaiqi
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Can anybody suggest which books are good for Lagrangian/Hamiltonian formulations for continuum beyond The Classical Mechanics by Goldstein ( it seems a bit too complicated for my understanding.)?
 
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check out classical mechanics by John R Taylor, i have heard its a very good book.
 
Hamiltonian299792458 said:
check out classical mechanics by John R Taylor, i have heard its a very good book.
Thanks for your suggestion. I browsed Chapter 16 roughly, but it seems to have no relation to Lagrangian/Hamiltonian formulation.
 
There are only a few books, where the Lagrangian formalism is used in continuum mechanics, I'm aware of. Of course, my all-time favorite for classical physics, A. Sommerfeld, Lectures on Theoretical Physics, vol. 2 has a section on it for both incompressible and compressible ideal fluids.

For the relativistic case, you find it in a very elegant way in Soper, Classical Field Theory.
 
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vanhees71 said:
There are only a few books, where the Lagrangian formalism is used in continuum mechanics, I'm aware of. Of course, my all-time favorite for classical physics, A. Sommerfeld, Lectures on Theoretical Physics, vol. 2 has a section on it for both incompressible and compressible ideal fluids.

For the relativistic case, you find it in a very elegant way in Soper, Classical Field Theory.
I think these two books are too hard for me to follow. Any other suggestions?
I found Scheck's Mechanics chapter 7 is a good introduction. Any other books alike?
 
Last edited:
robphy said:
Marsden & Hughes might be useful
https://authors.library.caltech.edu/25074/1/Mathematical_Foundations_of_Elasticity.pdf

The website of Darryl Holm may also be interesting:
http://wwwf.imperial.ac.uk/~dholm/classnotes/
I found below:
Hamill : A Student's Guide to Lagrangian and Hamiltonians.
Mann,Peter: Lagrangian & Hamiltonian dynamics
Fetter,Walecka: Theoretical Mechanics of particles and continua
Florian Scheck: Mechanics, From Newton's Laws to Deterministic Chaos
But all these books use one chapter/section(about 20 pages) to illustrate. I felt it not enough yet.
Besides, Florian Scheck's Classical Field Theory may be of help.
Any other books talking about it in detail?
 
thaiqi said:
I found below:
Hamill : A Student's Guide to Lagrangian and Hamiltonians.
Mann,Peter: Lagrangian & Hamiltonian dynamics
Fetter,Walecka: Theoretical Mechanics of particles and continua
Florian Scheck: Mechanics, From Newton's Laws to Deterministic Chaos
But all these books use one chapter/section(about 20 pages) to illustrate. I felt it not enough yet.
Besides, Florian Scheck's Classical Field Theory may be of help.
Any other books talking about it in detail?

I guess books on classical field theory may talk about it. Any such books on classical field theory?
 
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jasonRF said:
A very detailed 2-volume monograph has been written by Berdichevsky. I have only flipped through it very briefly - it is certainly a graduate level text
https://www.amazon.com/Variational-Principles-Continuum-Mechanics-Fundamentals/dp/3540884661
https://www.amazon.com/Variational-Principles-Continuum-Mechanics-Applications/dp/3540884688

I haven't looked at Goldstein's treatment, but I suspect Berdichevsky isn't any easier.

jason
Thanks.
I think these two books may be of help:
Auria & Trigiante: From Special Relativity to Feynman Diagrams
Susskind: Special Relativity and Classical Field Theory: The Theoretical Minimum
 
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