Timeline for Calculus of variations -- how does it make sense to vary the position and the velocity independently?
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 2, 2016 at 7:00 | history | edited | user36790 | CC BY-SA 3.0 |
added 127 characters in body
|
| Nov 22, 2015 at 13:10 | comment | added | TheQuantumMan | @grizzlyadam so in the end, they are not independent but can be treated as much because the mathematics prove it, right? | |
| Jan 14, 2011 at 15:57 | comment | added | wsc | "Not a word of Landau, not a thought of Lifshitz." | |
| Nov 17, 2010 at 19:55 | comment | added | Sklivvz | Landau is a great mathematical physicist but he's not known as a simple writer :-) | |
| Nov 17, 2010 at 17:02 | comment | added | grizzly adam | Yes, the notation is confusing. That's another problem. | |
| Nov 17, 2010 at 9:34 | comment | added | Greg Graviton | ... and to express the variations $\delta u$ and $\delta v$ in terms of $\delta x$ afterwards. | |
| Nov 17, 2010 at 9:33 | comment | added | Greg Graviton | The notation for the arguments $L$ is somewhat confusing, in which case it is instructive to consider the following example: take $F(x,2x-y)$ and vary $F(x+\delta x,2(x+\delta x)-y) = \frac{\partial F}{\partial x}\delta x + \frac{\partial F}{\partial (2x-y)}2\delta x$. You might say that the arguments of $F$ are varied independently, but that sounds weird. If anything, it's just that the notation for the partial derivatives of $F$ is bad; it is much better to write $F(u,v)$ and $(u,v)=(x,2x-y)$ to obtain $\delta F = \frac{\partial F}{\partial u}\delta u + \frac{\partial F}{\partial v}\delta v$ | |
| Nov 17, 2010 at 9:30 | comment | added | Greg Graviton | Well, instead of saying "$q$ and $\dot q$ are varied independently", you could also say "$q$ and $\dot q$ are varied (perhaps independently, perhaps not)" and later note that the variation $\delta\dot q$ is given by $\delta\dot q = \frac d{dt} \delta q$. | |
| Nov 17, 2010 at 6:25 | history | edited | grizzly adam | CC BY-SA 2.5 |
added 140 characters in body; added 16 characters in body
|
| Nov 17, 2010 at 6:19 | history | answered | grizzly adam | CC BY-SA 2.5 |