Timeline for How is the Euler-Lagrange equation derived without local coordinates?
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| Dec 13, 2017 at 12:17 | comment | added | Francois Ziegler | @Tyson 1) I posted “that” because as I said, it corrects your erroneous characterization of the vector field. Its contraction with the 2-form is not $dL$ but $-dH$ where $H$ is the Hamiltonian. 2) What matters in differential geometry is that results be coordinate-free. Better come to terms with the fact that not all proofs can or need to be. (E.g.: existence of the exterior derivative.) 3) That said, I think Souriau’s formula (7.28) (= 6th displayed in Cartan’s §184) gives about as close to an intrinsic argument as you’ll get. Call them “completely wrong” at your own risk :-) | |
| Dec 12, 2017 at 21:43 | comment | added | Tyson | The last link does not give a complete answer but it is helpful. Other links however like Cartan and souriaou are just completely wrong , they are as far from coordinate free as possible i dont know why you posted that. | |
| Dec 9, 2017 at 16:52 | history | edited | Francois Ziegler | CC BY-SA 3.0 |
added 109 characters in body
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| Dec 9, 2017 at 15:50 | history | answered | Francois Ziegler | CC BY-SA 3.0 |