Analyzing a Static System using Lagrangian Mechanics

AI Thread Summary
The discussion focuses on analyzing a static system using Lagrangian mechanics, specifically to find the weights of points A and B, as well as the friction coefficient for A on a horizontal plane. The weights are determined to be equal, with P_A and P_B both equal to Q/2, and the friction coefficient is found to be 1. The Lagrangian is defined as L = T - u, where T is kinetic energy and u is potential energy, and the relevant equation is provided for analysis. The user expresses frustration with the clarity of the textbook and the professor's teaching style, indicating a lack of understanding regarding degrees of freedom and generalized variables. Overall, the thread highlights the challenges of applying Lagrangian mechanics to a static system while seeking clarity in the educational material.
TheDestroyer
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Hi guyz, I taked the picture attached with my mobile directly from the book, please help me to find the weights of A,B (not masses), and the friction coefficient (f) for A on the Horizontel plane, and note, the rope isn't able to change lenght, System is static, A,B are equal, weight of K is Q

NOTE : I NEED TO FIND THE SOLUTION OF THIS SYSTEM USING THE ANALYTICAL MECHANICS AND LAGRANGES EQUATION (NOT THE NEWTONIAN VECTOR MECHANICS)

The Answer is:
P_A = P_B = \frac{Q}{2}
f=1

Lagranges equation:

\frac{d}{dt} \frac{\partial L}{\partial \dot{q}} - \frac{\partial L}{\partial q} = 0

L = T - u

L is the langrangian, T is kinetic energy, u is potential energy, q is generalized coordinate,
 

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First, how many degrees of freedom are there?
Second, what generalized variables would you like to define?
 
Only what i have written, i don't know how many freedom degrees, the question has only the information A = B, K weight is Q, and that diagram,

I'M NERVOUS OF THAT PROFRSSOR, HE MADE THAT BOOK STUPIDLY, IF YOU SAW IT YOU WILL KILL HIM, NOTHING IS CLEAR !
 
Well? No one answered! Should we say I have fools book?
 
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