Talk:Maupertuis's principle

Reduced action
Hi Willow,

This may drive you nuts, but take a look at the "energy of a curve" in the article metric tensor. linas 01:40, 19 July 2006 (UTC)

Leibniz's Priority
"The present scholarly consensus seems to be that the quotations from Leibniz are indeed genuine". Without a reference this is worthless babble. — Preceding unsigned comment added by 82.56.19.136 (talk) 7 August 2006 (UTC)

Mass Tensor
This article refers to "The Mass Tensor" which is not defined anywhere. Please can we have a definition? CosmoPeter (talk) 09:11, 24 March 2013 (UTC) — Preceding unsigned comment added by CosmoPeter (talk • contribs) 08:43, 24 March 2013 (UTC)

Input?
Is "input" a well established term? Why isn't "domain" used as a more commonly understood synonym?

In the section Mathematical Formulation, what do you think of changing "Note that the abbreviated action S0 is not a function, but a functional, i.e., something that takes as its input a function (in this case, the path between the two specified states) and returns a single number, a scalar." to "Note that the abbreviated action S0 is not a function, but a functional, i.e., something that has as its domain all differentiable functions (in this case, the path between the two specified states) and produces a Real single number, a scalar."

I am not sure to what order the functions have to be differentiable (once differentiable, twice differentiable,..., smooth). (All differentiable functions are continuous and integrable, of course.) I am also not sure that limiting the range to Reals is correct.

Comments?Abitslow (talk) 16:25, 21 December 2013 (UTC)


 * I am not opposed to calling something that takes functions (of some sort or other) to numbers a "functional".


 * But nobody with adequate mathematical training would claim that such things are "not functions".


 * It is clear to me that whoever wrote the article does not understand some very basic mathematical definitions and language, even if they fully understand how to explain it in their own words. 2601:200:C000:1A0:549:A1C6:F28A:53D2 (talk) 04:09, 9 November 2022 (UTC)
 * (An understanding of mathematical definitions and language is not a prerequisite to contribute to these pages. The key criteria is to have references so the next editor can verify the content and make improvements.)
 * The issue discussed here is no longer an issue as the text does not say "not functions". Johnjbarton (talk) 16:06, 15 November 2023 (UTC)

Please don't say "generalized" this and "generalized" that.
It is a very bad idea to use a word that has a large number of vaguely defined meanings — like "generalize" — to define a technical term.

But these technical terms ("generalized coordinates" and "generalized velocities") are completely unnecessary.

Worse: They are only confusing.

Here is why: The coordinates are coordinates of the state space (or phase space, or configuration space). That's what the word "coordinates" means. So there is no reason to call them "generalized".

The velocities are velocities simply because each one is the derivative of some parametrization of a curve. That's what a velocity means in mathematics. So there is nothing generalized here. 2601:200:C000:1A0:2979:6874:1986:631D (talk) 03:51, 9 November 2022 (UTC)