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

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The discussion centers on the notation L(v^2) as presented in Landau & Lifshitz's book on mechanics. The key takeaway is that L is a function solely of the velocity vector magnitude squared, denoted as v^2, and does not depend on position (r) or time (t). This clarification is crucial for understanding the dynamics described in the text, particularly in the context of deriving equations related to motion.

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hagopbul
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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
 
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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##.
 
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