Chronology Current Month Current Thread Current Date
[Year List] [Month List (current year)] [Date Index] [Thread Index] [Thread Prev] [Thread Next] [Date Prev] [Date Next]

Re: [Phys-l] Landau on Lagrangian

I happen to have started re-reading L&L's mechanics treatise just the other day, and wasn't too happy with their treatment, for the same reasons you brought it up. However, upon reading Lawrie's approach, and then going back and reading L&L's again, I don't object so much to the Landau approach. They're really similar, though I think Lawrie's arguments are a little clearer (perhaps just for being much more abbreviated; I normally like a lot of rigor and discussion about sticking points and generalizations).

I've just checked in Weinberg's "Gravitation and Cosmology"; he's another author who normally explicitly mentions such sticking points, but I didn't see this particular issue. Fetter and Walecka's "Theoretical Mechanics" defines T as a quadratic in qdot, but goes no further. I am going to look at Sean Carroll's lecture notes (I think -- I can't remember exactly) on GR, because I think he might carefully go through these arguments.

Morse and Feshbach, whom I normally quite like for their insights, seem to say (section 3.2 on Hamilton's Principle) only "No matter how the q's are chosen, the kinetic energy of an inertial system always turns out to be a quadratic function of the qdot's." I've also checked some more specialized texts (Kolmogorov, e.g., and some others) and no one explicitly addresses this. Maybe Lawrie's statement that he knows of no other reason other that it always seems to work is as "satisfactory" as it gets.

/************************************
Down with categorical imperative!
flutzpah@yahoo.com
************************************/




________________________________
From: Stefan Jeglinski <jeglin@4pi.com>
To: Forum for Physics Educators <phys-l@carnot.physics.buffalo.edu>
Sent: Thu, January 21, 2010 10:41:40 AM
Subject: Re: [Phys-l] Landau on Lagrangian

Ian D. Lawrie, in his "A Unified Grand Tour of Theoretical Physics",
Sections 3.1 and 3.2, goes through the arguments in a much more
pleasing fashion (in my opinion) than L&L. His steps are:

Thanks for this summary. In fact, Landau does touch on these items in
the periphery, albeit as you suggest in not quite the same explicit
detail. I am seeing the greater importance of the Galilean transform
now.


Stefan Jeglinski
_______________________________________________
Forum for Physics Educators
Phys-l@carnot.physics.buffalo.edu
https://carnot.physics.buffalo.edu/mailman/listinfo/phys-l