Calculating Rod Movement with Lagrangian Mechanics: Shear Modulus & Mass Ratios

AI Thread Summary
The discussion revolves around calculating the movement of a rod using Lagrangian mechanics, specifically focusing on the relationship between shear modulus and mass ratios. The user seeks assistance in formulating the Lagrangian for a cantilevered rod influenced by a heavy block, emphasizing the need to understand how forces are transferred from the block to the rod. They express uncertainty about how to relate the material properties, such as shear modulus, to the motion of the rod when an impulse is applied. Additionally, they request recommendations for resources or literature that could aid in solving the problem. The conversation highlights the complexities of modeling dynamic systems in mechanics.
danesh
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Hi!
I want to calculate the movement of the rod in the picture, but I don't know how to put up the Lagrangian for the problem.
I have the Shear modulus, \mu, for the material and M>>m and \theta = 0. I need the Lagrangian and from there on I think I can manage with the calculations myself.

Thanks
 

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Can you post the wording of the problem.
 
Gamma said:
Can you post the wording of the problem.
Well, I have come up with the problem myself.
What I am trying to get is an equation for the motion of the rod, or cantilever if you will. My problem is that I am not sure how to relate the force influencing the heavy block the rod is attached to, to the rod.
I think I need to make a connection between the Shear modulus, or the elasticity modulus of the material the rod and the block is made of to the force which is transferred to the rod.

I will settle for some help using usal mechanics on how the force is transferred from the block to the rod.

Thanks
 
Ok, let me refrase my question a bit.
Can somebody tell me how the rod goes about to "sway" when a impulse is applied on the bigger block with mass M?
If you know a book or a homepage, which you could refer me to for this problem, I would apperciate that as well.
 

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