Lagrangian: How did they get from this step to the other?

  • Thread starter unscientific
  • Start date
  • Tags
    Lagrangian
In summary, the conversation discusses the differentiation of the equation m\ell\dot{\theta}\cos{\theta} and the confusion over the third term in the first equation of 5.192. The conclusion is reached that the second and third terms come from differentiating the mentioned equation and there are two terms due to the presence of two \theta's. The confusion is resolved and understanding is gained.
  • #1
unscientific
1,734
13

Homework Statement


wi7wg9.png

Homework Equations


The Attempt at a Solution


I don't understand where the third term from the first equation of 5.192 come about.. as clearly L doesn't depend on x at all, so ∂L/∂x should be zero.

sc75p1.png
 
Last edited:
Physics news on Phys.org
  • #2
The second and third terms both come from differentiating the [itex]m\ell\dot{\theta}\cos{\theta}[/itex] term...you get two terms because there are two [itex]\theta[/itex]'s in it.
 
Last edited:
  • #3
Chopin said:
The second and third terms both come from differentiating the [itex]m\ell\dot{\theta}\cos{\theta}[/itex] term...you get two terms because there are two [itex]\theta[/itex]'s in it.

ah that makes sense! thanks alot!
 

1. What is the Lagrangian and what is its purpose?

The Lagrangian is a mathematical function used in classical mechanics to describe the motion of a system. It is used to find the most probable path that a system will take from one point to another, and is based on the principle of least action.

2. How is the Lagrangian derived?

The Lagrangian is derived from the principle of least action, which states that the path a system will take is the one that minimizes the action, a quantity that describes the total energy in a system. The Lagrangian is calculated by taking the difference between the kinetic and potential energies of a system.

3. What are the steps involved in using the Lagrangian to solve a problem?

The first step is to identify the system and its constraints. Next, the Lagrangian is calculated by finding the kinetic and potential energies of the system. Then, the Euler-Lagrange equations are used to find the equations of motion. Finally, the equations are solved to find the most probable path of the system.

4. Can the Lagrangian be used in any system?

The Lagrangian can be used in any system that can be described by a set of coordinates and has a well-defined potential energy. It is commonly used in classical mechanics, but can also be applied in other areas of physics such as quantum mechanics and field theory.

5. Are there any limitations to using the Lagrangian?

While the Lagrangian is a powerful tool for solving problems in classical mechanics, it does have some limitations. It assumes that the system is conservative and that all forces are derived from a potential energy. It also cannot be used in systems with non-conservative forces, such as friction or air resistance.

Similar threads

  • Advanced Physics Homework Help
Replies
5
Views
1K
  • Advanced Physics Homework Help
Replies
2
Views
979
Replies
5
Views
2K
  • Advanced Physics Homework Help
Replies
5
Views
2K
Replies
7
Views
2K
Replies
25
Views
2K
  • Advanced Physics Homework Help
Replies
1
Views
2K
  • Advanced Physics Homework Help
Replies
24
Views
2K
  • Advanced Physics Homework Help
Replies
5
Views
2K
  • Advanced Physics Homework Help
Replies
3
Views
907
Back
Top