Equations of motion using Lagrange

In summary, the individual is seeking help with finding equations of motion for a problem given by their professor. They are struggling with the exercise and have provided their attempts, but are unsure about their Lagrangian. They ask for assistance in understanding the correct approach and apologize for their English skills. Additionally, they request that equations be written in LaTeX format for clarity.
  • #1
PaulaFrafa
1
0
Hi, my professor asked me to proove the equations of motion of a problem. The equations that I need to find are in page 2 of the file https://docs.google.com/file/d/0BxOdCfkh6FqpUlY5TktpbDZTc2M/edit , equations 7 and 8. But, I'm having trouble with the exercise.

I uploaded my attemps. Problably I'm wrinting a wrong Lagrangian.. Does anyone have a clue about the right way? Sorry for my english, I'm not a native speaker. Thanks
 

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  • #2
Can you please write your equations in latex as per forum rules?
Than perhaps I will understand what you are asking, as the link provided leads me to a page that has no equations. (I couldn't turn the page.)

For example, we can write the lagrangian of a system,$$\mathcal{L}(q, q', p, p')$$ by writing the following
\mathcal{L}(q, q', p, p')
If you prefer dot notation,
$$\mathcal{L}(q,\dot{q},p,\dot{p})$$
Where the dots are made by \dot{variable}
Ie,
$$\dot{a}$$
Double dot can be done as well,
$$\ddot{a}$$
For more specific see the FAQ.
Note: you must put "$$" at the beginning and end of the statement as it makes the forum recognize it as latex.
Cheers,
 
Last edited:

Related to Equations of motion using Lagrange

1. What is the principle of least action in Lagrangian mechanics?

The principle of least action states that the true path of a physical system is the one that minimizes the action, which is defined as the integral of the Lagrangian function over time. This principle is used to derive the equations of motion for a system in Lagrangian mechanics.

2. How are Lagrangian equations of motion different from Newton's laws of motion?

While Newton's laws of motion are based on forces acting on a system, the Lagrangian equations of motion are derived from the principle of least action and involve the concept of energy. In Lagrangian mechanics, the equations of motion describe the evolution of a system in terms of its kinetic and potential energy, rather than the forces acting on it.

3. What is the role of generalized coordinates in Lagrangian mechanics?

Generalized coordinates are used to describe the configuration of a system in Lagrangian mechanics. They are chosen based on the degrees of freedom of the system and can be any set of independent parameters that uniquely determine the state of the system. In contrast to Newton's laws, which use Cartesian coordinates, Lagrangian mechanics allows for a more convenient and generalized description of a system's motion.

4. How are Lagrangian equations of motion derived?

The Lagrangian equations of motion are derived using the principle of least action and the Lagrangian function, which is defined as the difference between the kinetic and potential energy of a system. The equations are obtained by taking the variation of the action with respect to the generalized coordinates and their time derivatives, and then solving for the equations of motion.

5. What are some advantages of using Lagrangian mechanics over Newton's laws?

One advantage of using Lagrangian mechanics is that it can simplify the analysis of complex systems by reducing the number of variables needed to describe the system's motion. It also allows for a more elegant and generalized approach to solving problems in mechanics, making it useful in various fields such as physics, engineering, and mathematics.

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