Is Routh Function a non-relativistic KK theory?

[arivero]

I have just read a mention about a variant of Legendre transformation that instead of producing the Hamiltonian produces "Routh function", and that the some of this coordinates in this function are interpreted as extra coordinates producing the potential energy.

It sound very like Kaluza Klein, where the extra coordinates produce the force fields (and thus the potential energy). How valid is this analogy? Will KK theory produce Routh Theory in the non relativistic limit?

Generically, is there some modern information on this formalism?

 

[UltrafastPED]

Do you mean Routh's ignorable variables? If not please provide a reference ... I'm familiar with the removal of cyclic variables, but not the generation of extra variables.

 

[arivero]

Yep, I think I mean that, ignorable variables. Regretly I have only seen, till now, the mention in Felix Klein "history of mathematics in the XIXth century".

 

[UltrafastPED]

In that case the answer to your first question is "no".

The Routh procedure is usually taught in an advanced course in classical mechanics; you can find it in most advanced texts like Goldstein's "Classical Mechanics", or most other graduate texts.

 

[arivero]

Thanks for the answer. Still... does Goldstein mention explicitly the idea of a "purely kinetic" theory to be obtained from Routh technique?

 

[UltrafastPED]

I don't recall. When writing my monograph on analytical mechanics I decided to omit Routh as off the mainline of development. Hertz did develop a purely kinetic theory ...at least he started it prior to his untimely death.

 

[arivero]

Ok, thanks very much. I will try to follow these leads.

It is mostly a curiosity, but at least it tells that Kaluza was not doing a surprising move by using extra variables in his theory. People nowadays believes that extra dimensions are invented in string theory :-D