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

[thaiqi]

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.)?

 

[Hamiltonian]

check out classical mechanics by John R Taylor, i have heard its a very good book.

 

[thaiqi]

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.

 

[vanhees71]

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.

 

[thaiqi]

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?

 

[robphy]

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/

 

[thaiqi]

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]

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?

 

[jasonRF]

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

 

[thaiqi]

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

 

[atyy]

https://www.amazon.com/dp/0486432610/?tag=pfamazon01-20
Theoretical Mechanics of Particles and Continua
Alexander L. Fetter & John Dirk Walecka

https://www.amazon.com/dp/0471595519/?tag=pfamazon01-20
Classical Field Theory: Electromagnetism and Gravitation
Francis E. Low

 

[robphy]

https://www.amazon.com/dp/0201416255/?tag=pfamazon01-20
Noel Doughty
Lagrangian Interaction: An Introduction To Relativistic Symmetry In Electrodynamics And Gravitation

https://www.amazon.com/dp/0486650677/?tag=pfamazon01-20
Cornelius Lanczos
The Variational Principles of Mechanics

 

[thaiqi]

https://www.amazon.com/dp/0201416255/?tag=pfamazon01-20
Noel Doughty
Lagrangian Interaction: An Introduction To Relativistic Symmetry In Electrodynamics And Gravitation

https://www.amazon.com/dp/0486650677/?tag=pfamazon01-20
Cornelius Lanczos
The Variational Principles of Mechanics

Thanks for all of you.