Generalized force and the Lagrangian

In summary, the problem involves finding the generalized force and Lagrangian equation of motion for a particle sliding without rolling down an inclined plane. The method suggested by the teacher is to use the work done to account for the friction force. The angle of the inclined plane can be represented as theta and other necessary parameters can be used.
  • #1
Hiranya Pasan
30
3

Homework Statement


A particle of mass m slides without rolling down on a inclined plane, Find the generalized force and the Lagrangian equation of motion of mass m.

Homework Equations


T = (mx'^2)/2
Generalized force Q=-d/dx(V)

The Attempt at a Solution


To find the generalized force first I found the Potential energy and taking the derivative with the x, but my teacher said that the friction force should take into the account therefore I was told using the Work done, find the generalized force. How can I do that?
 
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  • #2
Your issues seem to suggest there is more to the problem than what you state. Please post the entire problem statement quoted word by word.
 
  • #3
Orodruin said:
Your issues seem to suggest there is more to the problem than what you state. Please post the entire problem statement quoted word by word.

Thanks for the response , This is the entire probelm, but the angle of inclined plane can be taken as theta and we can take parameters as necessary
 
  • #4
help :(
 

1. What is the concept of generalized force in physics?

Generalized force is a concept in classical mechanics that describes the force acting on a system in terms of its generalized coordinates. It takes into account all the forces acting on a body, including external forces and constraint forces.

2. How is generalized force related to the Lagrangian formulation?

In the Lagrangian formulation, generalized force is used to derive the equations of motion for a system. It is the derivative of the system's potential energy with respect to its generalized coordinates.

3. What is the significance of the Lagrangian in physics?

The Lagrangian is a fundamental concept in classical mechanics that describes the dynamics of a system. It is a mathematical function that summarizes the kinetic and potential energies of a system, and is used to derive the equations of motion.

4. How is the Lagrangian different from the Hamiltonian?

While the Lagrangian describes the dynamics of a system in terms of its generalized coordinates and velocities, the Hamiltonian describes the same dynamics in terms of the generalized coordinates and momenta. The Hamiltonian is derived from the Lagrangian using a mathematical transformation known as the Legendre transformation.

5. Can the Lagrangian be used to study systems with constraints?

Yes, the Lagrangian formulation is particularly useful for studying systems with constraints, as it takes into account all the forces acting on a system, including those from constraints. This allows for a more comprehensive understanding of the system's dynamics and can simplify the equations of motion in certain cases.

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