Hello, everybody. I'm looking for some reference about the Poincaré-Cartan form, I do not know how it is defined, I just know that it is used in Lagrangian mechanics but I have not found any references. Can you advise me a book that deals with the topic?
In particular I would be interested to know who invented the forms of Poincaré-Cartan.
Thank you very much.
Best Answer
You could try the introductory sections of our book, "Exterior Differential Systems and Euler-Lagrange Partial Differential Equations" (authors Bryant, Griffiths, Grossman), which is available at http://arxiv.org/abs/math/0207039. There are definitions, discussions, and references to the older literature there.
There is also considerable material in Giaquinta and Hildebrandt "Calculus of Variations", but it's not near the front.
Another place you can look is in the works of Ian Anderson and/or Peter Olver and their students.