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

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The discussion centers on the L(v^2) notation in Landau & Lifshitz's Mechanics, specifically on pages 4-5. It clarifies that L is a function of the velocity vector v, not dependent on position r or time t. The notation indicates that L is expressed as a function of the magnitude of the velocity squared, |v| = √(v^2). This understanding helps in deriving related equations, such as equation (3.1). The conversation emphasizes the importance of grasping this notation for further comprehension of the mechanics presented in the book.
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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