Talk:Lagrangian

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[edit] Old comments

  • Can someone please explain where \partial_\mu came from? -- Taral 17:38, 17 Jun 2004 (UTC)
\partial_\mu (shorthand for \frac {\partial}{\partial x^\mu}) crops up here instead of \frac{d}{dt} that you see in, for example action, because the function that is being varied, \ \phi(x) is a function of 'n' variables xμ (μ = 1,2,3 ... n) as opposed to q(t) which is a function of 1 variable t. -- Amar 10:03, Jun 18, 2004 (UTC)
Agree. Will try and attempt a merge sometime soon. [[User:AmarChandra|Amar | Talk]] 09:14, Jul 28, 2004 (UTC)
If no one objects, I'll add the content of this page to Lagrangian mechanics and set up a redirect here. - mako 30 June 2005 00:19 (UTC)
  • Can someone explain why is the spelling "Lagrangian" preferred here to "Lagrangean"? I would expect the pattern "Shakespeare -> Shakespearean".
I would suspect the difference is time period. Shakespeare -> Shakespearean was probably a valid English formation for a significant period of time. Lagrange lived more recently by ~200 years, when Lagrange -> Lagrangian was probably favored.
Personally, I had never even considered "Lagrangean" as an option, but apparently it is sometimes used: Google search turns up 1:27 for Lagrangean:Lagrangian. --Laura Scudder 16:54, 3 Apr 2005 (UTC)
Isn't it because Lagrangean is pronounced with a hard g, so to keep the soft j sound it's spelled Lagrangian? Fephisto 17:19, 30 December 2006 (UTC)
Well, usually when one refers to a function or object, one uses (-ian), e.g. Lagrangian or Hessian or Jacobian or Wronskian or Hamiltonian. So you guys are probably right that we should talk about Lagrangean mechanics, just as we talk about Euclidean geometry, but then there is also Riemannian geometry and Minkowskian geometry, and having to talk about a Lagrangian when dealing with Lagrangean mechanics would just be awkward. This is just the way physicists mangle words.
Just a note, the term Lagrangian is much newer than the object itself. In older literature it is just called Lagrange's function. :) --Lionelbrits (talk) 18:17, 27 November 2007 (UTC)

[edit] Functional

Is the Lagrangian itself a functional? It doesn't seem to be by the definition given. It's the expression for the action that's a functional, mapping a set of functions onto R. It's true that the coordinates that are the domain of the Lagrangian can be expressed as funtions of some parameter, but I'm not sure if that really makes the Lagrangian a functional; it certainly seems to be a differant case from the action integral.

I'm not confident enough to change this, and there do seem to be multiple definitions of functional, which confuses things. Comments? --Starwed 14:42, 14 December 2005 (UTC)

By the only definition of functional I know, it is indeed the action, not the Lagrangian that is a functional. I'll be bold and see if anyone comes up with another definition. — Laura Scudder ☎ 15:23, 14 December 2005 (UTC)

[edit] Vote for new external link

Here's my site full of PDE's with harmonic functions. Someone please put it in the external links if you think it's helpful!

http://www.exampleproblems.com/wiki/index.php/Calculus_of_Variations

[edit] Conflict of interest

Like User:Linas, I am concerned about recent edits by the data.optics.arizona.edu anon of this and other articles, edits which present the work of B Roy Frieden as mainstream. In fact, this work is not universally accepted and has been severely criticized (google for sci.physics.research discussion from some years ago, for starters). The conflict of interest is that this anon has confessed to being B. Roy Frieden IRL:

Notable edits by the data.optics.arizona.edu anon include:

  1. 150.135.248.180 (talk · contribs)
    1. 20 May 2005 confesses to being Roy Frieden in real life
    2. 6 June 2006: adds cites of his papers to Extreme physical information
    3. 23 May 2006 adds uncritical description of his own work in Lagrangian and uncritically cites his own controversial book
    4. 22 October 2004 attributes uncertainty principle to Cramer-Rao inequality, which is potentially misleading
    5. 21 October 2004 adds uncritical mention of his controversial claim that Maxwell-Boltzmann distribution can be obtained via his "method"
    6. 21 October 2004 adds uncritical mention of his controversial claim that the Klein-Gordon equation can be "derived" via his "method"
  2. 150.135.248.126 (talk · contribs)
    1. 9 September 2004 adds uncritical description of his work to Fisher information
    2. 8 September 2004 adds uncritical description of his highly dubious claim that EPI is a general approach to physics to Physical information
    3. 16 August 2004 confesses IRL identity
    4. 13 August 2004 creates uncritical account of his work in new article, Extreme physical information

---CH 21:25, 16 June 2006

[edit] Inaccessible

This article is not very accessible because the equations are not explained in words, such as the equation that shows that S does not change (which is an assumption based on conservation of energy I suppose). Also the different forms of the differential are not clear. I haven't been able to find the meaning of reverse wiggle d for example, which closes me out of a proper understanding. As I recall this is a post grad level d symbol, so it is not reasonable to expect a person to know it. --Centroyd 02:41, 22 July 2007 (UTC)

The action does not change because you can show that \frac{\delta}{\delta q_i} S \left(q_i) \right) leads to the Euler-Lagrange equation, which is zero. That's where the zero comes from. It's all covered in action (physics). The δ symbol is usually used to indicate a small but non-differential change. It's probably used here to remind us that we're changing a functional, which requires we jump through some extra hoops. — Laura Scudder ☎ 14:47, 22 July 2007 (UTC)
The δ indicates that the differential is a virtual displacement differential. A force acting through a virtual displacement does virtual work. Virtual displacements are not functions of time (time is taken to be held constant when considering virtual displacements). When (1) the only net applied forces to a system are defined by scalar potentials (i.e. they are conservative), and when (2) the inertial forces are used to to convert a dynamic system into a static system, and when (3) the generalized coordinates are chosen to match the internal degrees of freedom of the system, then the principle of virtual work for applied forces says that the constraints do no virtual work (because they act normal to the paths of the virtual displacements), that the difference of the inertial and applied forces also does no virtual work because the system is in static equilibrium, and that the system operates in accordance with Lagrange's equation. Sorry this isn't more detailed, but this is just a talk page. The reference I got this information from is: Torby, Bruce (1984). "Energy Methods", Advanced Dynamics for Engineers, HRW Series in Mechanical Engineering (in English). United States of America: CBS College Publishing. ISBN 0-03-063366-4.  ChrisChiasson 20:25, 22 September 2007 (UTC)

[edit] Brackets for functional dependence

Since this seems to be the subject of some edits and reverts, perhaps the opposing parties could offer their comments here. I will say that, as an observer, the brackets for functional notation look dumb (that's just my opinion - no offense, hopefully). ChrisChiasson (talk) 14:35, 22 November 2007 (UTC)

Clarity is paramount in communication. It is more important to get the message across without mistakes than to adhere to the most common practice. While it is more usual to use parenthesis to indicate functional dependence than to use brackets, the use of parenthesis runs the risk that the reader will confuse it with the use of parenthesis to indicate grouping — the precedence order of operations. Also there is the risk that the reader will think that the two items are to be multiplied rather than that one is a function of the other.
In advanced books, these problems are often avoided by omitting mention of the functional dependence since the reader is assumed to know that the quantities are dependent variables. However, in Wikipedia, I think that we should not make such an assumption. JRSpriggs (talk) 01:10, 24 November 2007 (UTC)
Yeah, this is the notation I've always seen when clarity on functional dependence is needed. Yes, it looks silly, but it is the most transparent. — Laura Scudder ☎ 13:34, 24 November 2007 (UTC)
This seems to be a complete dumb informalism. See the page of Action (physics). The lagrangean is somethimes writeen using [] and sometimes ().

This ilogical formalism (informalism) that is valid for some examples and invalid for others. If the use of () is more suitable for the reader to read, it can be used without misunderstandment. There is no formalism like ( use parenthesss for it and brackets for that.)

I can use without misunderstanding (1+(2+(3+(4))) prefered by {1+[2+(4)]}

Util it is formalized in a proper way, it is more logical to be used in a way to please the reader.

[edit] Lagrangian Mechanics

This article says "This article is about Lagrange mechanics" -- then why is there a separate article called Lagrangian Mechanics? Why isn't that article linked here, or at the Lagrangian (disambiguation) page? PenguiN42 (talk) 19:45, 1 February 2008 (UTC)

This article does link to that one — in the sentence "Under conditions that are given in Lagrangian mechanics, ..." in the lead. If you want to put an additional link on the disambiguation page, be my guest. JRSpriggs (talk) 07:03, 3 February 2008 (UTC)