Question about L(v^2) Notation in Landau & Lifshitz's Mechanics

[hagopbul]

Hello :

i am reading now landau & lifshitz book on mechanics and i have small question :

about L(v^2) notation it was not very clear in the book and i couldn't understand it correctly anyone can explain it or provide a link with explanation
page (4 - 5)

Best regards
Hagop

 

[anuttarasammyak]

Do you have a problem to derive (3.1) ? I understand :

L is function of only $\mathbf{v}$, not of $r$ and t. Further L is function of $|\mathbf{v}|=\sqrt{v^2}$. Thus L is function of $v^2$.