Using Lagrangian and Euler to Analyze the Falling Stick Problem

[Raziel2701]

Homework Statement

A meter stick stands on a frictionless surface and leans against a frictionless wall as shown. It is released to fall when it makes an angle of 1 degree from the vertical. Use Lagrange and Euler to find how long it takes the stick to fall to the ground.

The Attempt at a Solution

The potential of the stick will essentially just be mgL correct? Since the stick starts from an angle of 1 degree.

The Kinetic energy would have two components, a rotational and a translational. For rotation, I guess I'll just use $$\frac{1}{2}I\omega^2$$. I guess I could look up the moment of inertia later on but I want to get the setup right.

For translational kinetic energy, when the stick falls, the center of mass of the stick falls down but it also moves horizontally, so there's an x and y component to the velocity so the KE would be $$\frac{1}{2}mv^2$$

What concerns me is that v should be x-dot squared and y-dot squared but then it seems like I have too many variables for an object that has two(?) degrees of freedom.

How do I set this up?

 

[Raziel2701]

Ok I realized a few things that are very hard to grasp for me. Mainly, understanding how we can describe the problem requires such a feel for the problem that I request some links, or books that deal with this method(Lagrangian method).

So the center of mass describes a circle in its motion so the only degree of freedom is governed by the angle correct? The potential would also be different now, it should be mglcos(theta).

I'm going back to work on this, I'll come back if I need more help but I'd still like some more references to read up and study if you'd be so kind.