As part of a larger problem I need to prove that the following equation is a function of time. I guess that means I must get rid of the partial derivatives and replace them with total derivatives?
I have the following relationships from electromagnetism:
I have been battling this for over a week!
Here is the whole problem:
Calculus of Variations Rund Trautman Electromagnetism Problem
A,V,x and x dot are all functions of time.
I think I need to show that a function F exists such that
Now terms 2 and 4 are clearly only functions of t.
I can manipulate term 3 to get:
Now term 1 is my problem
And if I'm not mistaken I do that by getting rid of the partial derivaties?
Using the equation for E I get:
Now the RHS of this looks remarkibly (but not quite) like the total derivative of A. The next equation is not correct (I don't think) but it is the sort of thing I need to get to?
Zeta and Tau come from
They come from
and a similar equation for zeta.
This problem comes from Example 4, here: Emmy Noether's Wonderful Theorem: Dwight E. Neuenschwander: 9780801896941: Amazon.com: Books