Talk:Analytical mechanics

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Merging Analytical Mechanics into Dynamics (mechanics)[edit]

Do not agree. I think these two disciplines have very different styles, and although commonly regarded as concerning the same subject matter, Analytical Mechanics seems to me to be much more general, sort of a frame-theory, an abstract formalism, rather than a theory about a determinate content. I seem to vaguely recall, in this respect, dealing in early college with electromagnetic phenomena using Analytical Mechanics' formalism! Again, I think they should be kept separate, at least for now. Will be, hence, removing the merger tag. --Aqualung 11:51, 15 March 2007 (UTC)

And before anyone comes back to this: I strongly disagree with merging this article into any other. Please leave it alone - NOT just because of my re-write; because IT IS a notable topic in its own right and there are plenty of articles within the scope of this one which all need a central summary. Of course there will be overlap between things, but that’s not a reason for pulling every single related article into one long, unreadable mash of formalism... F = q(E+v×B)ici 10:40, 22 June 2012 (UTC)

Use this article as an intro + overveiw[edit]

This article should contain the bulk of the qualitative details, leaving all (most of) the maths to the rest. D’Alembert, Lagrangian, Hamiltonian, etc formalisms are all very closely interlinked so this article can easily contain all these and provide all the links. F = q(E+v×B) ⇄ ∑ici 15:32, 18 April 2012 (UTC)

I extended the article completely, and pretty much defeated some of my own point above. For this article to be a summary of terminology, equations, definitions, etc. the maths needs to be here, but there are no derivations and everything is linked in excruciating detail - all further details are left to the main articles. Hopefully any confusion the lay reader may have between "phase space" and "configuration space", what the commutators and Poisson brackets are and their connection, or "Hamilton's characteristic/principle functions" in addition to the one defined by the Lagrangian, and how such little things with their own articles all link together into the framework of analytical mechanics, has been outlined and clarified neatly... F = q(E+v×B)ici 10:36, 22 June 2012 (UTC)

Hamiltonian Formulation is more general[edit]

"The Hamiltonian formulation is more general, allowing time-varying energy, identifying the path followed to be the one with stationary action."

There is a section that states the above. I'm not an expert, but the expression below appears to be an action formulated with respect to a Lagrangian, and my understanding is that the Hamiltonian conserves energy, rather than allowing it to vary, so the statement above seems to be false. Perhaps the word "Hamiltonian" should be replaced by "Lagrangian"? (talk) 03:06, 24 May 2015 (UTC)

Actually the Lagrangian and Hamiltonian equations are equivalent, whatever you can do in one you can in the other. I think in the section you mention "Hamiltonian Formulation" really refers to "Hamiltonian principle", one version of the principle of least action. I'll simplify the wording. M∧Ŝc2ħεИτlk 08:38, 24 May 2015 (UTC)