Introduction to the Lagrangian form of classical mechanics

[jack47]

I've been trying to find a good introduction to the Lagrangian form of classical mechanics. Preferably something I can get over the web, since I'm not at Uni this year. I might like something particularly slow

 

[MiGUi]

H. Goldstein's Classical Mechanics has an excellent treatment of analythical mechanics in his book. I'm not sure about the English title since my book is the spanish version, but this book is really good.

Bye.

 

[Allday]

Goldstein is the standard graduate university text. Its helpfull to have some other books around for different perspectives. Two books that I really liked are Classical Mechanics by Tai L. Chow and The Variational Principles of Mechanics by Cornelius Lanczos. Chow covers Newtonian and Langrangian/Hamiltonian stuff. Lanczos speaks a lot about the beauty and change of perspective that comes from treating mechanics without vectors. However these are not available on the web (for free). There's a text called motion mountain that is freely available that I haven't had the time to check out.

 

[Dr Transport]

There are many sets of notes out there on the web to guide you. Try looking on this website for links, Physics Napster is a good place to go

https://www.physicsforums.com/showthread.php?t=31

Goldstein is the best at a graduate level, Marion/Marion&Thorndike or Fowler are the standards at the ug level. Dated is the Schaum's outling in Lagrangian Dynamics, but I learned quite a bit from it, just takes time.

dt

 

[rocketcity]

I think Marion and Thornton is the way to go. I pity anyone who had to learn from the venerable Goldstein without Marion and Thornton to back him up. I also think M. Boas' introduction to the variational principle (upon which Lagrangian mechanics is based) is invaluable.

The Euler-Lagrange equation is easy to apply to many systems that you've probably already analyzed ad nauseum using Newtonian mechanics (F=ma and all that).

The Lagrangian L of a system is defined as its kinetic energy MINUS its potential energy (L = T - V). At this point, you should comment to yourself that this resembles the total energy, which is T + V (or so we've been told), and leave it at that. Also, in general T will be a function of velocity but not position, and V a function of position but not velocity. The exceptions prove the rule.

Write an expression for L for a simple system--I like (1) a body in free-fall at the Earth's surface, (2) a mass on a 1-D tabletop attached to a Hooke spring, and (3) a rigid pendulum (small angle approximation, too.) The E-L eqn says that

d/dt of (dL/dv) = (dL/dx)

By 'v' I mean x-dot, the time derivative of x. x, of course, stands for whatever coordinate appears in your expression of the Lagrangian. In my three examples, there's only one 'x' in each Lagrangian.

Plug 'em in and see what you get!

P

 

[robphy]

I posted some links for Lagrangian Mechanics on another thread

https://www.physicsforums.com/showpost.php?p=202444&postcount=5

 

[hhegab]

You can for sure try Schaum's book "Theoretical Mechaincs" this is a very good book and full with problems that will clarify things to u. give it a try.

hhegab

 

[Gokul43201]

Goldstein, by itself, is not a whole lot of fun.

 

[pmb_phy]

I've been trying to find a good introduction to the Lagrangian form of classical mechanics. Preferably something I can get over the web, since I'm not at Uni this year. I might like something particularly slow

Don't bother with Schaum's or Goldstein. Schaum's assumes that you've taken an upper level mechanics course at the university level and Goldstein is a graduate text. Neither of those are useful for someone who is not at an university level. The best that I can direct you to on the internet is the Harvard lecture notes at

http://www.courses.fas.harvard.edu/~phys16/handouts/textbook/ch5.pdf

Enjoy!

Pete

 

[jack47]

Thanks for all the responses guys :)

And particular thanks go to pmb phy, for giving me EXACTLY what I wanted (a good first course in Lagrangian mechanics available on the web)