Lagrangian linear masses (CM)

In summary, a Lagrangian linear mass is a mathematical model used in physics to describe the motion of a system of particles. It simplifies the equations for calculating the motion and allows for the incorporation of constraints in a more efficient manner. The center of mass (CM) is used as a reference point in this model. It can also be applied to systems with non-linear motion by using a more complex Lagrangian function. However, the model has limitations such as assuming constant mass for each particle, which may not accurately describe certain systems.
  • #1
mamou6262
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Homework Statement


A combination of masses along the z-axis is separated by a distance 'a' with middle mass at origin. The potential is
[tex] V = \frac{1}{2}kx^2 [/tex].
What is the force of constraint using Lagrange multiplier?

Homework Equations


[tex] L = T - V + \lambda f[/tex]


The Attempt at a Solution


I found L and calculated the lagrange eqn of motions but still I am getting
[tex] m \ddot{z} - \lambda = 0 [/tex]

z is not moving, so [tex] \ddot{z} = 0 [/tex].
Based on this [tex] \lambda = 0 [/tex]
Is the question wrong?
 
Last edited:
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  • #2
You should get 3 equations of motion, one for each coordinate (x,y,z)
 

Related to Lagrangian linear masses (CM)

What is a Lagrangian linear mass?

A Lagrangian linear mass is a mathematical model used in physics to describe the motion of a system of particles. It takes into account the position, velocity, and acceleration of each particle in the system.

How is the center of mass (CM) related to Lagrangian linear masses?

The center of mass (CM) is a point within a system of particles that represents the average position of all the particles. In the Lagrangian linear mass model, the CM is used as a reference point for calculating the motion of the particles.

What are the advantages of using Lagrangian linear masses in physics?

One advantage of using Lagrangian linear masses is that it simplifies the equations for calculating the motion of a system of particles. It also allows for the incorporation of constraints, such as forces acting on the system, in a more efficient manner.

Can Lagrangian linear masses be applied to systems with non-linear motion?

Yes, the Lagrangian linear mass model can be extended to systems with non-linear motion by using a more complex Lagrangian function that takes into account the non-linearities in the system.

Are there any limitations to using Lagrangian linear masses?

One limitation of the Lagrangian linear mass model is that it assumes each particle in the system has a constant mass. This may not accurately describe certain systems, such as those involving particles with varying mass or systems with continuous distributions of mass.

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