Analyzing a Static System using Lagrangian Mechanics

In summary, the conversation is about a problem involving finding the weights of A and B, as well as the friction coefficient, using analytical mechanics and Lagrange's equation. The system is static and A and B are equal. The Lagrangian is defined as the difference between kinetic and potential energy, and the question asks about the degrees of freedom and generalized variables. The speaker also expresses frustration with the book and lack of clarity in the problem.
  • #1
TheDestroyer
402
1
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:
[tex]P_A = P_B = \frac{Q}{2}[/tex]
[tex]f=1[/tex]

Lagranges equation:

[tex]\frac{d}{dt} \frac{\partial L}{\partial \dot{q}} - \frac{\partial L}{\partial q} = 0[/tex]

[tex]L = T - u[/tex]

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

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  • #2
First, how many degrees of freedom are there?
Second, what generalized variables would you like to define?
 
  • #3
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 !
 
  • #4
Well? No one answered! Should we say I have fools book?
 

Related to Analyzing a Static System using Lagrangian Mechanics

1. What is analytical mechanics?

Analytical mechanics is a branch of classical mechanics that uses mathematical techniques and equations to study and explain the motion and behavior of physical systems. It is concerned with the principles of motion and the forces that cause it.

2. What is the difference between analytical mechanics and classical mechanics?

Classical mechanics is a broader field that encompasses both analytical mechanics and Newtonian mechanics. While classical mechanics uses primarily geometric and algebraic methods to study motion, analytical mechanics uses advanced mathematical techniques such as calculus and Lagrangian formalism.

3. What is the importance of analytical mechanics in physics?

Analytical mechanics provides a more comprehensive and elegant approach to understanding the behavior of physical systems compared to classical mechanics. It also allows for the study of complex and non-linear systems that cannot be accurately described using Newtonian mechanics.

4. What are some practical applications of analytical mechanics?

Analytical mechanics has numerous applications in various fields, including engineering, astrophysics, and robotics. It is used to design and analyze systems such as satellites, aircraft, and mechanical structures. It is also essential in the study of celestial mechanics and the motion of celestial bodies.

5. What are some key concepts in analytical mechanics?

Some key concepts in analytical mechanics include the principle of least action, Hamiltonian mechanics, and Lagrangian mechanics. Other important principles include the conservation of energy, momentum, and angular momentum. These concepts are used to analyze and predict the behavior of physical systems and are essential in understanding the laws of motion.

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