Re: [Phys-l] Landau on Lagrangian

[Brian Whatcott <betwys1@sbcglobal.net>]

Stefan Jeglinski wrote:
> >  > Why not :
> >  > Ergo: L=L( | v | )   ?
> >     
>
> Indeed.
>
>
>   
> > 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).
> >     
>
> OK, but the spirit of the question survives, unless I misunderstand 
> you. In the "first principles" approach that's been discussed in this 
> thread, the argument does not appear to preclude one from supposing 
> the free classical particle Lagrangian to be (1/2)m|v|. This would 
> seem justified (Occam's Razor?), other than the rather glaring 
> inability to get N2, which takes us back ultimately to the only 
> argument left: "in our universe, this apparently just doesn't seem to 
> be the case."
>
>
> Stefan Jeglinski
Interesting topic. One can suppose that the experiment to support the 
idea that energy of [downwards] translation is proportional to distance 
is very accessible.
One can suppose that it is also reasonable to suppose that such a 
movement is accelerating.
But if so, it would be hard to support the proposition that the energy 
gained
is proportional to both distance and velocity.

Brian W