Talk:Lagrangian mechanics

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Possible error in the introduction using the terms ″variation″

In the introduction of this page the term $\delta {\mathcal {S}}:[t_{0},t_{1}]\rightarrow \mathbb {R}$ is defined and called the ″variation″, which is possibly erroneous (although $\delta {\mathcal {S}}$ is indeed a Gateaux derivative). Comparing $\delta {\mathcal {S}}$ with the definition of ″variation″ (of $x_{0}$ ) in the Wikipedia page virtual displacement, one finds instead that a variation is a function as well of the parameter ε. In other words, the "variation" is not equal to the "Gateaux derivative". However, it might be that the term "variation" is defined in some other way (which is then inconsistent with the definition in virtual displacement). Doubledipp (talk) 16:45, 16 April 2022 (UTC)Doubledipp[reply]

There is some discrepancy between math and physics in how the term "variation" is used. In math,

\delta {\cal {S}}

could have been (and is in some sources) called infinitesimal variation. StrokeOfMidnight (talk) 06:46, 20 April 2022 (UTC)[reply]

Lead section rewritten

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)[reply]

Suggestion about

"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)[reply]

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

Source for nightmares

@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:

Parsons, Paul; Dixon, Gail (2016). 50 ideas you really need to know : science. London: Quercus. pp. 4–7. ISBN 9781784296148.

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)[reply]