Anyway I am now clear with my doubt. 2T - H is another form of L so basically it's the same as L. I was interested in only T + V. Thank you for your valuable responses.
I know that by extremizing lagrangian we get equations of motions. But what if we extremize the energy? I am just little bit of confused, any help is appreciated.
Oh, similar way of expansion, calculations on 547, are done. In Jackson's (p.547) equation such as (11.94) , (11.96), (11.98) are expanded by Taylor expansion.
Now I got it. I was thinking in very different way. First one was easy, and second one is essentially taylor expansion. But here we are just taking approximation, thank you all of you.
yes doubts are questions.
Oh, I come to know about the first part but still for second question how is it possible to have metric tensor equal to exponential of metric tensor?
In Jackson, (3rd edition p. 545), there are equations they are given as,
$$A = e^L $$
$$det A = det(e^L) = e^{Tr L}$$
$$g\widetilde{A}g = A^{-1} $$
$$ A = e^L , g\widetilde{A}g = e^{{g\widetilde{L}g}} , A^{-1} = e^{-L}$$
$$ g\widetilde{L}g = -L $$
I have several doubts.
1) $$det(e^L) =...
Myself doing physics undergraduate in college. I have many doubts some concepts and want to clear them. Hope this community is as good as stackexhange.