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

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)