Talk:Lagrange bracket

From Wikipedia, the free encyclopedia

[edit] "Definition" is flawed

MathSciNet search produced only a handful of mentions of "Lagrange brackets". According to a few of them, a Lagrange bracket is an analogue of Poisson bracket in the case of a contact manifold. The review to the following paper outlines their origin and mentions that they "have fallen out of use":

Iglesias, Patrick, Les origines du calcul symplectique chez Lagrange [The origins of symplectic calculus in Lagrange's work], L'Enseign. Math. (2) 44 (1998), no. 3-4, 257--277 MR1659212.

A.P. Soldatov (2001), “Lagrange bracket”, in Hazewinkel, Michiel, Encyclopaedia of Mathematics, Kluwer Academic Publishers, ISBN 978-1556080104  reproduces the same formula as the article here, but is a bit more careful about the nature of these expressions. As far as I could tell, they are the components of the symplectic form with respect to the pair of (non-canonical) coordinates u, v. I am going to edit the article to make it more mathematically meaningful. Arcfrk 01:33, 15 August 2007 (UTC)

Go for it, you know this kind of stuff better than I do. I had never heard about them so I'm not surprised to hear that they have fallen out of use. I don't understand what you mean with "they are the components of the symplectic form with respect to the pair of (non-canonical) coordinates u, v" though; u and v are only two variables so they can't be used as coordinates? By the way, my edit was prompted by reading two pages of the cited book (via Google Books) which does not form a good basis to understand the concept. -- Jitse Niesen (talk) 02:29, 15 August 2007 (UTC)

The text you wrote in the article itself is very clear. Thanks. -- Jitse Niesen (talk) 05:13, 15 August 2007 (UTC)