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

AI Thread Summary
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
Messages
397
Reaction score
45
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
 
Last edited:
Physics news on Phys.org
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##.
 
Last edited:
  • Like
Likes hagopbul and vanhees71
Hello everyone, Consider the problem in which a car is told to travel at 30 km/h for L kilometers and then at 60 km/h for another L kilometers. Next, you are asked to determine the average speed. My question is: although we know that the average speed in this case is the harmonic mean of the two speeds, is it also possible to state that the average speed over this 2L-kilometer stretch can be obtained as a weighted average of the two speeds? Best regards, DaTario
This has been discussed many times on PF, and will likely come up again, so the video might come handy. Previous threads: https://www.physicsforums.com/threads/is-a-treadmill-incline-just-a-marketing-gimmick.937725/ https://www.physicsforums.com/threads/work-done-running-on-an-inclined-treadmill.927825/ https://www.physicsforums.com/threads/how-do-we-calculate-the-energy-we-used-to-do-something.1052162/

Similar threads

Replies
24
Views
2K
Replies
10
Views
5K
Replies
2
Views
1K
Replies
7
Views
680
Replies
2
Views
797
Replies
8
Views
4K
Back
Top