I've got here so far, but first of all I'm not sure if i did it right till the last line and second, if I've been right, i do not know what to do with the rest.
should i consider each of levi-civita parentheses in the last line zero?
and one additional question about the term in the first line...
i don't know why i haven't tried differentiating it when its written in form of field tensor!
so if I'm not wrong with my calculations(cause i got the hint from your advice but i couldn't follow the rest of yours and tried writing it down for myself again) in the end, with considering coulomb's...
Homework Statement: finding equation of motion for Born-Infeld lagrangian
Homework Equations: born-infelf lagrangian
i do not know where I'm going wrong.
i'll be really grateful for any advice.