How Do I Start Solving a Lagrangian Mechanics Problem?

[bombz]

Homework Statement

http://img85.imageshack.us/gal.php?g=hw1y.jpg

Its an imageshack gallery

Homework Equations

Book gives completely irrelevant equations.

The Attempt at a Solution

I couldn't even solve A. I have no clue how to start this. The instructor isn't providing any assistance and it's not a book problem meaning, book equations are completely irrelevant.
Please help . I need guidance. If could solve it and then help me step by step with explanation, that would be great :) thank you!

 

[fzero]

When you say you couldn't do part A, what was your confusion? Taking the partial derivatives? Identifying F_i? It's easy to say you're completely confused, but you should try to explain what little bit that you do understand.

 

[vela]

This problem is pretty much just grinding through some math. You're given a Lagrangian

$$L=\frac{1}{2}m_1\dot{x}_1^2+\frac{1}{2}m_1\dot{x}_2^2-\frac{k}{|x_1-x_2|}$$

and the Euler-Lagrange equations

$$\frac{\partial L}{\partial x_j} - \frac{d}{dt}\,\frac{\partial L}{\partial \dot{x}_j} = 0$$

For part (a), plug that Lagrangian you're given into the Euler-Lagrange equation. You'll end up with a term like $m_j\ddot{x}_j$ in your result. Isolate it. What it's equal to is F_j.

Treat the coordinates and velocities as independent variables, and it will simplify things if you write the potential as

$$V(x_1,x_2) = \frac{k}{|x_1-x_2|} = \frac{k}{\sqrt{(x_1-x_2)^2}}$$

to get rid of the absolute value.

If you're getting stuck, post your work so we can see how and where you're getting stuck or going wrong.

 

[bombz]

This problem is pretty much just grinding through some math. You're given a Lagrangian

$$L=\frac{1}{2}m_1\dot{x}_1^2+\frac{1}{2}m_1\dot{x}_2^2-\frac{k}{|x_1-x_2|}$$

and the Euler-Lagrange equations

$$\frac{\partial L}{\partial x_j} - \frac{d}{dt}\,\frac{\partial L}{\partial \dot{x}_j} = 0$$

For part (a), plug that Lagrangian you're given into the Euler-Lagrange equation. You'll end up with a term like $m_j\ddot{x}_j$ in your result. Isolate it. What it's equal to is F_j.

Treat the coordinates and velocities as independent variables, and it will simplify things if you write the potential as

$$V(x_1,x_2) = \frac{k}{|x_1-x_2|} = \frac{k}{\sqrt{(x_1-x_2)^2}}$$

to get rid of the absolute value.

If you're getting stuck, post your work so we can see how and where you're getting stuck or going wrong.

Oh my gosh. Thank you so much! exactly what I was looking for. I worked through it so well with your help. THUMBS UP!