Talk:Lagrangian mechanics

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Was redirected to Talk:Lagrange's equations.

Definitely needs a rewrite. A lot of the content here overlaps with the content in action (physics), but the derivation of the Euler-Lagrange equations differs. Some consolidation is probably in order, and I think I prefer the one here to the one in action (physics). There's definitely a notational issue, since this page uses r' and the other uses r-dot.

Taral 08:13, 19 Jun 2004 (UTC)

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I have trouble understanding this bit below:

More generally, we can work with a set of generalized coordinates and their time derivatives, the generalized velocities: {q_j, q′_j}. r is related to the generalized coordinates by some transformation equation:

What is q

What is this equation?

The above equation makes no sense what so ever.

I cleared it up a bit, I hope, by reordering that sentence and adding a really simple example. Laura Scudder 00:08, 7 Mar 2005 (UTC)

Great article. But since the biggest clincher is generalized coordinates, perhaps there should be separate discussion on the matter elsewhere? --Rev Prez 13:10, 28 May 2005 (UTC)

"Generalized coordinates", according to Landau & Lifshitz, refers to any s quantities q₁,q₂,...,q_s which completely define position in a system with s degrees of freedom. "Generalized velocities" are the associated velocities. You can think of them as vectors. For example, in a 3D system, which has three degrees of freedom, the usual way to think about the q variables are x, y and z. The Lagrangian works in spherical and cylindrical coordinate systems as well, which may be why the "generalized" label is used. - mako 30 June 2005 00:25 (UTC)

The generalized coordinates are really about picking the coordinates that make your life easiest. For instance, simple problems often have lower dimensional motion embedded in 3 dimensions, so you don't actually need 3 generalized coordinates. It all depends on whether the constraints on the motion are holonomic or not. So the generalized reminds you that your coordinates may need to be a totally non-traditional system, like the length along a wire bent into a weird shape (perhaps a bead is moving along the wire). --Laura Scudder | Talk 30 June 2005 01:16 (UTC)

[edit] generalized coordinates

The link generalized coordinates links to this page (Lagrange mechanics), I believe it would be nice to have either a larger discussion of generalized coordinates on this page or perhaps its own article. Article could give examples (such as how they are used in cartesian or spherical-polar coordinates) and discuss the relation to degrees of freedom. Perhaps a discussion on the related generalized momenta. Ideas? 71.131.37.89 02:37, 21 December 2005 (UTC)

[edit] gen. coord. added

Generalized coordinates now have their own article, which is not 100% yet, but is a good start. I'll continue to work on it and parse the content between this page and that over the next week.Jgates 03:13, 25 December 2005 (UTC)

• As pointed before, nice article, however i find this lack on several "rare" but sometimes common examples involving Lagrangians:

L(q,q',q'',t) (Lagrangian with an acceleration term)

and the usual Hamiltonian Mechanics, i think in this case Hamiltonian is given by:

xp' + x'p'' − H(q,p,p') = L

these Hamiltonians happens in the euler-Lagrange equations for GR see "Ray D'inverno: Introducing Einstein's Relativity" (university course in Cosmology )