- #1
jostpuur
- 2,116
- 19
I always like to do the variational calculations in rigor way for example like this
[tex]
0 = D_{\alpha} \Big(\int dt\; L(x(t)+\alpha y(t))\Big)\Big|_{\alpha=0} = \cdots
[/tex]
because this way I understand what is happening. However in literature I keep seeing the quantity
[tex]
\delta x(t)
[/tex]
being used most of the time. What does this delta mean really? Does it have a rigor meaning? It seems to be same kind of mystical* quantity as the [itex]df[/itex], but this time an... infinite dimensional differential?
*: mystical in the way, that even if the rigor meaning exists, it is not easily available, and the concept is usually used in non-rigor way.
[tex]
0 = D_{\alpha} \Big(\int dt\; L(x(t)+\alpha y(t))\Big)\Big|_{\alpha=0} = \cdots
[/tex]
because this way I understand what is happening. However in literature I keep seeing the quantity
[tex]
\delta x(t)
[/tex]
being used most of the time. What does this delta mean really? Does it have a rigor meaning? It seems to be same kind of mystical* quantity as the [itex]df[/itex], but this time an... infinite dimensional differential?
*: mystical in the way, that even if the rigor meaning exists, it is not easily available, and the concept is usually used in non-rigor way.