Talk:Lagrangian mechanics#L for Lagrangian.2C script for density

I've rewritten the lead section per MOS:INTRO to get rid of the equations and the more complicated mathematical language. All of that stuff appears later in the article, and the lead needs to provide a less technical overview of the topic.PianoDan (talk) 20:05, 25 April 2022 (UTC)

"Any variation of the functional gives an increase in the functional integral of the action."

Delete this sentence and discuss saddle point in the sentence before it. 210.61.187.232 (talk) 11:07, 17 June 2024 (UTC)

:I deleted the sentence. Johnjbarton (talk) 15:01, 17 June 2024 (UTC)

@WikieMouse added this paragraph

• Analyzing the behaviour of complex dynamical systems was nightmarishly complicated until the emergence of Lagrangian Dynamics - for example, calculation of the motion of a swinging pendulum since the time-varying constraint forces like the friction of the wire, the tension of the pendulum rod, the drag in the air, etc. - Lagrangian dynamics uses the principle of least action proposed by Pierre de Fermat to explain the the properties of light waves.

Adding this source:

• {{Cite book |last=Parsons |first=Paul |title=50 ideas you really need to know : science |last2=Dixon |first2=Gail |publisher=Quercus |year=2016 |isbn=9781784296148 |location=London |pages=4-7 |language=en}}

What does the source talk about, the last sentence, or every aspect of the paragraph? I know that Lagrangian dynamics profoundly altered theoretical analysis but this is first I've heard that it also had similarly fundamental effects on practical applications. Johnjbarton (talk) 18:11, 23 September 2024 (UTC)

:This is what the source said, although I would say I rephrased it a little and added an example. And as far as I know, Lagrangian mechanics does make calculating practical things much more easier than Newtonian mechanics since it only makes use of a set of generalized equations. I stand mine although I could be a little wrong, you see I am not an experienced editor yet. WikieMouse (talk) 11:22, 26 September 2024 (UTC)

::@WikieMouse I think different kinds of physics problems are more easily tackled in one framework or another. While not commonly covered in introductory physics, each approach adopts certain criteria for solutions. Newtonian mechanics focuses on forces and a single point in time, trying to predict motion in the next instant. Thus when the forces are known and the goal is predicting a small increment in time, the technique is superior to all others. Conversely integral methods like Lagrangian mechanics are based on energy and are much better at answering global questions like the time course of a pendulum. Johnjbarton (talk) 15:23, 26 September 2024 (UTC)

:::That's what I am saying! There is nothing wrong in my paragraph. I got the necessary stuff covered. WikieMouse (talk) 09:30, 27 September 2024 (UTC)

:I don't know if this is because the additions could be better written or because the source (I have no access to it) got things wrong, but it doesn't make much sense to me. A swinging pendulum is not a very complex system. What is the friction of the wire? Though there are tricks to write lagrangians for some non-conservative forces, their main use is for the conservative ones (with well-defined potentials). Where are we "completely summing the overall paths of possible motion of the particles"? Langrangian mechanics (people) are least concerned with path integrals when solving their problems. I don't think any engineers use langrangians. The Fermat principle note disrupts the flow of the text, it's also a little ambiguous. Revert, find better sources? Ponor (talk) 11:23, 27 September 2024 (UTC)

::I am very sorry, let me change my example so that you're more happy. WikieMouse (talk) 12:18, 27 September 2024 (UTC)

::Alright I changed the paragraph, have a look and tell me if it needs anything else. WikieMouse (talk) 14:15, 27 September 2024 (UTC)

:::I added a ref and made some changes. BTW the variational principle that leads to the principle of least action is a separate concept. It is an extension of the Lagrangian approach. See eg Action principles. Johnjbarton (talk) 15:55, 27 September 2024 (UTC)

::::Thanks for the correction. WikieMouse (talk) 17:01, 27 September 2024 (UTC)

@EditingPencil, please add sources, thanks. Johnjbarton (talk) 15:41, 3 February 2025 (UTC)

:I had tried for a few minutes and given up, so apologies for not having added a cn tag already. I've added it now and if my edit affect readability or usefulness I don't mind if it is reverted/edited. I do know that the proof is straight forward and that this is how constraints are used in solving problems as well, so I only need to find a source which maybe more effort than I can do currently. EditingPencil (talk) 17:48, 3 February 2025 (UTC)

::I've quickly copied it into my sandbox here, so moving the topic over there is a solution. I have there some extra related stuff that I haven't bothered to do much, too. Feel free to take any call! EditingPencil (talk) 17:59, 3 February 2025 (UTC)

::Hand and Finch or Goldstein should have anything worth putting in this article and more. If these sources don't have stuff, we need to consider if it should be added. Johnjbarton (talk) 18:47, 3 February 2025 (UTC)

:::I think the page could benefit from more detail on the use of Lagrange multipliers:

:::* the intuitive interpretation

:::* motivation for their use in practice

:::* description of how the resulting system of equations are DAEs

:::* show how to solve for lambda as a matrix equation

:::I've made some very rough snipits in my sandbox.

:::(references only listed at the bottom for the moment)

:::Any thoughts @EditingPencil @Johnjbarton? DrBrandonJohns (talk) 16:15, 21 June 2025 (UTC)

::::Don't you think such content belongs in Lagrange multipliers? Johnjbarton (talk) 19:25, 21 June 2025 (UTC)

:::::I've thought about it some more. I think you're right that it's too much for this page.

:::::I think instead to go for more cross-linking between pages, each getting a few small edits instead of one getting a big edit.

:::::* Lagrange_multiplier#Applications could use a short statement linking to Lagrangian_mechanics, including the motivation and interpretation

:::::* DAEs#Examples already has a Lagrangian mechanics example. Solving for lambda might fit well there.

:::::* For this page, I think there is value re-adding what @EditingPencil did in their sandbox, along with a short cross-link to DAEs.

:::::For the reference @EditingPencil was looking for, it is described by Goldstein, and in even more detail by [https://doi.org/10.1007/978-3-540-45677-3 A. I. Lurie]

:::::Does this sound better? DrBrandonJohns (talk) 07:33, 22 June 2025 (UTC)

::::::Yes, that sounds great. Johnjbarton (talk) 16:14, 22 June 2025 (UTC)