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

To be sure!
I merely wanted to point out that Landau's treatment (even if accepted as valid) does not demonstrate that the translational kinetic energy must be proportional to the SQUARE of the speed.
The opposite is easily (but incorrectly) inferred from the presentation.

Bob Sciamanda
Physics, Edinboro Univ of PA (Em)

From: "David Bowman" <>
Sent: Thursday, January 21, 2010 5:34 PM
To: "'Forum for Physics Educators'" <>
Subject: Re: [Phys-l] Landau on Lagrangian

Regarding Bob S's objection:

. . . L must also be independent of the direction of v, and is
therefore a function only of its magnitude, i.e. v^2."
Ergo: L = L(v^2) .

Why not :
Ergo: L=L( | v | ) ?

No generality is lost here. Note that |v| is a function of v^2. In particular |v| = sqrt(v^2). So any real function of |v| is also a real function of v^2 as well (because a function of a function is a function).

David Bowman
Forum for Physics Educators