I Understanding the Coordinates in the Lagrangian for a Pendulum

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The discussion focuses on understanding the coordinates used in the Lagrangian formulation for a pendulum, specifically referencing a solution from Landau's classical mechanics book. The coordinates for the support point and the mass are derived from the harmonic oscillator model, with the support point defined as ##\mathbf{r}_p = a(\cos{\gamma t}, -\sin{\gamma t})## and the radius vector from the support point to the mass as ##\mathbf{R} = l(\sin{\phi}, \cos{\phi})##. The final coordinates of the mass are a combination of these two vectors, leading to a clearer understanding of the pendulum's motion. The poster expresses gratitude for the clarification received. This exchange highlights the importance of visual aids and mathematical representation in grasping complex mechanics concepts.
p1ndol
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So I've been studying classical mechanics and have come across a small doubt with the solution provided to the problem in question from Landau's book. My question is: why are the coordinates for the particle given as they are in the solution? I imagine it has something to do with the harmonic oscillator, but I'd like to properly understand. I appreciate any kind of help, and I'm sorry if this post is somehow incorrect, it is my first one regarding questions.
 

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Did you look at the figure? For instance in (a), the support point ##p## has coordinates ##\mathbf{r}_p = a(\cos{\gamma t}, -\sin{\gamma t})## and the radius vector from ##p## to ##m## has coordinates ##\mathbf{R} = l(\sin{\phi}, \cos{\phi})## then the coordinates of ##m## are nothing but those of the vector ##\mathbf{r}_p + \mathbf{R}##.
 
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I understand it now, thanks!
 
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/
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