Talk:Hamilton's principal function

I have copied this article from here in order to have easy and direct link to it.--Gulmammad (talk) 20:49, 14 May 2008 (UTC)

This article resembles too closely the discussion made in Goldstein. Is this legitimate? —Preceding unsigned comment added by 80.30.150.145 (talk) 01:55, 26 May 2009 (UTC)

Actually the article (applications part) resembles closely the discussions made in almost all books on Classical Mechanics. Two of them, Goldstein and Landau are shown as refs. Zitterbewegung ^Talk 18:23, 27 June 2009 (UTC)

There is a $-t$ missing at the end of the following line:

$\beta ={\frac {\partial S}{\partial E}}=\int {\frac {m}{\sqrt {2mE-mkq^{2}}}}\,dq-t={\sqrt {\frac {m}{k}}}\sin ^{-1}{\sqrt {\frac {kq^{2}}{2E}}}$

Sigi_E, 27 June 2009

Yes, I fixed it. Zitterbewegung ^Talk 18:13, 27 June 2009 (UTC)

Actually, I don't think this article correctly defines the principal function itself (see Lanczos, The Variational Principles of Mechanics). It is supposed to be independent of all momenta (conserved and time-dependent, as well as the energy), unlike Jacobi's transformation functions, and depends only on the initial and final co-ordinates (including time). Hamilton's principal function is different to the Jacobi transformation functions, used to change between different co-ordinate systems. In most cases it cannot be compute directly, but is supposed to represent the "distance" between two points on the same hyperplane (H = E) in phase space, purely in terms of position. —Preceding unsigned comment added by 131.111.28.93 (talk) 10:44, 19 November 2010 (UTC)