Talk:2010 MAT495H1 Group: Calculus of Variations

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Some notes related to my 2010_05_12 appear in Chapter 5 of File:2000 Colliander 279.pdf. In particular, those notes contain some basic discussion about Hamilton's principle and about the passage from Lagrangian to Hamiltonian dynamics. I think it will also be instructive to work out a few other examples:

  • straight line is the shortest distance between two points in Euclidean space
  • geodesic is shortest distance between two points on a manifold
  • Brachistochrone problem; if possible also demonstrate the tautochrone property of the cycloid
  • Find best tunnel to dig through a homogeneous earth so that a frictionless train falling under gravity will make the trip in the shortest time. (Hypocycloid)
  • Develop some discussion of Nöther's theorem (see chapter 5 of [File:2000 Colliander 279.pdf]] or the Sulem-Sulem text. Another (more geometric) good presentation appears inside Shatah-Struwe text.

Hello everyone. I'm in the soliton group, but I'm myself reading about the calculus of variations this summer. If you have questions I may be able to answer them, so give me a try, either by posting on the wiki or in person on Wednesdays. --Jordanbell 19:05, 17 May 2010 (UTC)

To Prof. Colliander: It appears that discussions of geodesics, cycloids and the Euler-Lagrange equation have already been posted on the list of topics for this course. For these three topics, do we simply link to those pages, or do you want our group to create our own discussion? -- Baiyun 23:58, 17 May 2010 (UTC)

Yun Tao: Thanks for your message. Yes, I see that User: Peter has uploaded some content. I suggest that you add links to your group page to those pages and then, as a group, discuss the content posted there and convince yourselves you understand it. Is the notation consistent across the pages? Can you supplement it with other discussion? Are there questions to ask on the associated discussion pages? In short, I want your group to leverage everything they can find or study to master some aspects of the calculus of variations. Colliand 02:14, 18 May 2010 (UTC)

Hi calculus of variations group. An excellent set of notes on the calculus of variations are "Notes on functionals" by Ben Svetitsky, available on his webpage at http://giulio.tau.ac.il/~bqs/functionals/functionals.html I should have mentioned this earlier! --Jordanbell 03:23, 17 June 2010 (UTC)

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