Timeline for Geometry of Hamilton-Jacobi Equation
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 27, 2015 at 2:44 | answer | added | tom | timeline score: 5 | |
| Mar 27, 2015 at 2:38 | comment | added | tom | Actually, I don't think such general solutions could exist in this case, as every solution satisfies $S[\gamma_{ext}] = S(t_1,y_1)-S(t_0,y_0)$. This is a little surprising, but I know so little of the theory of FOPDEs I really have no right to be surprised here :) | |
| Mar 27, 2015 at 2:04 | comment | added | tom | @Qmechanic Thankyou once again! You've been very helpful, and I now feel my initial suspicions were completely vindicated: the converse is true, and solutions of the H-J equation do correspond to the minimal action from some particular point in phase space (or at least elements of the complete solution - there may be general solutions derived from envelopes of the complete solution which behave otherwise.) I'll explain my error (as usual, very silly) in an answer below. :) | |
| Mar 26, 2015 at 14:12 | comment | added | Qmechanic♦ | Related: physics.stackexchange.com/q/32268/2451 and links therein. | |
| Mar 26, 2015 at 13:59 | history | asked | tom | CC BY-SA 3.0 |