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!
 
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