Thanks for your suggestion. I browsed Chapter 16 roughly, but it seems to have no relation to Lagrangian/Hamiltonian formulation.Hamiltonian299792458 said:check out classical mechanics by John R Taylor, i have heard its a very good book.
I think these two books are too hard for me to follow. Any other suggestions?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 found below: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/
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?
Thanks.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
robphy said: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
The Lagrangian and Hamiltonian formulations are two different mathematical approaches used to describe the dynamics of a system. The Lagrangian formulation is based on the principle of least action, which states that a system will follow the path that minimizes the action integral. The Hamiltonian formulation, on the other hand, is based on the conservation of energy and uses the Hamiltonian function to describe the system's dynamics.
Some popular books on this topic include "Classical Mechanics" by Herbert Goldstein, "Mechanics: From Newton's Laws to Deterministic Chaos" by Florian Scheck, and "Lagrangian and Hamiltonian Mechanics" by M.G. Calkin. These books provide a comprehensive introduction to the concepts and applications of Lagrangian and Hamiltonian formulations for continuum.
Yes, there are several online resources available for learning about Lagrangian and Hamiltonian formulations. Some recommended websites include the MIT OpenCourseWare, which offers free online courses on classical mechanics and Lagrangian dynamics, and the Stanford Encyclopedia of Philosophy, which provides in-depth articles on the history and principles of these formulations.
Yes, the Lagrangian and Hamiltonian formulations can be applied to a wide range of continuum systems, including fluids, gases, and solids. These formulations are based on fundamental principles of mechanics and can be adapted to different types of systems by modifying the Lagrangian or Hamiltonian function accordingly.
Yes, these formulations have many practical applications in various fields such as physics, engineering, and mathematics. They are commonly used in the study of fluid dynamics, celestial mechanics, and quantum mechanics. They also play a crucial role in the development of new technologies, such as spacecraft navigation and control systems.