Talk:History of variational principles in physics

Fork

Uhh, I think its a bad idea to fork the article on principle of least action. I don't mind having an article with this title, but the latin and its translation should be covered in either that article, or this article, but not both. linas 00:33, 19 July 2006 (UTC)

Maupertuis' priority

The priority dispute around Maupertuis is discussed here and in Maupertuis principle. Is that topic notable for the principle -- which ended up with his name -- or here? Both seems one too many to me. Johnjbarton (talk) 00:25, 10 November 2023 (UTC)

I would suggest leaving that to Maupertuis principle but still give some recognition to Koenig here.--ReyHahn (talk) 13:40, 10 November 2023 (UTC)

The problem seems to be thrice as bad, check Stationary-action principle.--ReyHahn (talk) 12:30, 12 November 2023 (UTC)

Ok we're down to just the one in Maupertuis principle now, and of course in the bio.

I cut this out entirely but I also avoided "first" etc in the text here. Johnjbarton (talk) 16:15, 14 November 2023 (UTC)

Some additions that might help

Maybe some missing points in this history article are Dido's problem, Galileo's contribution, Jacob Bernoulli's contributions and d'Alembert's virtual work. ReyHahn (talk) 11:41, 12 November 2023 (UTC)

Principle of least action

I've not found the ref again, but evidently the "principle of least action" means two different things. Historically it meant the early versions of the variational principle. Later these were effectively renamed, eg "Maupertuis principle" for a least-length version. Later, after Feynman, it came to mean application of the variational principle generally to physics. It does not help that "variational" is generic and each form has quite different choices for fixed (boundary?) conditions and free ones. Johnjbarton (talk) 15:59, 12 November 2023 (UTC)

I found one of these comments, in Feynman https://www.feynmanlectures.caltech.edu/II_19.html

• “Also, I should say that is not really called the ‘action’ by the most precise and pedantic people. It is called ‘Hamilton’s first principal function.’ Now I hate to give a lecture on ‘the-principle-of-least-Hamilton’s-first-principal-function.’ So I call it ‘the action.’ Also, more and more people are calling it the action. You see, historically something else which is not quite as useful was called the action, but I think it’s more sensible to change to a newer definition. So now you too will call the new function the action, and pretty soon everybody will call it by that simple name."

However Feynman was also famous for not reading other people's work, so I'm not yet sure of his claim here. Johnjbarton (talk) 16:19, 13 November 2023 (UTC)

This is sorted in the section "Modern terminology".

Resolved

Johnjbarton (talk) 15:30, 20 November 2023 (UTC)

Hamilton and d'Alembert principle

@Johnjbarton: How d'Alembert "generalized" (past tense) Hamilton principle? If I understand correctly d'Alembert's principle is from the 18th century and Hamilton's principle is from the 19th century. Maybe d'Alembert should be discussed in a higher section. Also Hamilton principle is not linked or referred in the article. ReyHahn (talk) 17:47, 14 November 2023 (UTC)

You are correct. I guess I was reading into my source based on this line in D'Alembert's principle.

• D'Alembert's principle is more general than Hamilton's principle as it is not restricted to holonomic constraints that depend only on coordinates and time but not on velocities.

I need to look for a better source. Johnjbarton (talk) 01:45, 15 November 2023 (UTC)

Also I was lead off by the pages 92, 93 in "The variational principles of mechanics" by Lanczos, Cornelius, which expounds on the generality of d'Alembert principle, making it sound very much like something that must have come after Hamilton. Johnjbarton (talk) 01:51, 15 November 2023 (UTC)

Ok so d'Alembert is a variation related to virtual work rather the least action. I fixed my error, but I'm unsure if this is what we want. I would prefer to have the technical content in the concept article and just history here.

Goldstein also says later that this principle is used in conjunction with least action. Johnjbarton (talk) 03:03, 15 November 2023 (UTC)

Maybe d'Alembert's principle is more general than Hamilton's principle in the same sense that Newton's laws of motion are more general than Euler-Lagrange equations because they can handle a wider number of dissipative forces. However, for me that seems misleading in the sense that it makes Hamilton's principle or Euler-Lagrange equations seem less useful.--ReyHahn (talk) 10:53, 15 November 2023 (UTC)

I think d'Alembert's generalizes virtual work from statics to dynamics. So its not a 'least action' variational principle, but rather a different variational principle related to virtual work. (I stumbled upon the d'Alembert from the old version of the Stationary-action principle which is why my edits were incoherent).

We could:

• delete d'Alembert here, or
• add some history for virtual work and an explanation about two (or more) variational principle threads, or
• wait until work on my proposed Action principles helps sort out the 'action' related variational principles then tackle the more general category.

Johnjbarton (talk) 15:57, 15 November 2023 (UTC)

Based on Coopersmith's book (Lazy...) virtual work and d'Alembert belongs here (though not in Action principles).

I've added something about virtual work and I think this issue is fixed up now. Johnjbarton (talk) 19:46, 20 November 2023 (UTC)

Morse theory

From ignorance, is Morse theory used in physics? ReyHahn (talk) 15:21, 15 November 2023 (UTC)

I don't know one way or another. Johnjbarton (talk) 15:58, 15 November 2023 (UTC)

I decided to remove that section. The text about Morse theory section used to read:

The first clear general statements on whether the variational principle found minima or other extrema (e.g. a saddle point) were given by Marston Morse in the 1920s and 1930s, leading to what is now known as Morse theory. For example, Morse showed that the number of conjugate points in a trajectory equaled the number of negative eigenvalues in the second variation of the Lagrangian.

References

if somebody cares to explain its relation to physics, please be free to add it back.--ReyHahn (talk) 16:42, 15 November 2023 (UTC)

Merge in to History of classical mechanics?

Now that this article is better shape, I was looking at History of classical mechanics. It is short and almost nothing on the era that matters, beginning with Euler, Lagrange and Hamilton. Newton is handled better on other pages.

I wonder if we would have a stronger result if we combined these in to a single "History of classical mechanics".

Pro:

• One article to monitor/fix/improve.
• The classical mechanics history would include Lagrange, Hamilton, and friends.
• The seemingly obscure variational principle topics would be more visible?

Con:

• The narrative of the variational history would be lost or obscured in a chronological setting. We could try threading the narrative through the items, eg "This work on action principles was followed up by Hamilton, see #...".
• actual work needed.

Johnjbarton (talk) 01:53, 28 November 2023 (UTC)

I have mixed feelings about it. I am (weakly) inclined to say that the merge would certainly benefit the classical mechanics article. It is very unusual to have this very specific article about history of variational principles when we do not have history articles for some major branches of physics (like condensed matter or cosmology). On the other hand, clearly the relativistic and quantum mechanical action principles should not be discussed in a classical mechanics article.--ReyHahn (talk) 09:02, 28 November 2023 (UTC)