Lagrangian problem of a cylinder on inclined plane.

[crucifige]

Homework Statement

A cylinder on a inclined plane is rolling without slipping. Inclined plane is connected to wall with a spring and cylinder is connected to wall with a spring too. All frictions will be neglected, and all the given data has shown on the image below.

As seen above, k2 spring and cylinder is only moving at vertical axis which can be thought as y.

2. The attempt at a solution

First of all, i have doubts on generalized coordinates. I think only one generalized coordinate should be used and it should be y. I need to solve this problem with D'Alembert Principle and Lagrangian Dynamics.

Thank you in advance for your help.

 

[TSny]

Hello and welcome to PF!

You may use y as your generalized coordinate, but you don't have to. There are a couple of other possible choices for the generalized coordinate.

But you have the correct idea that there is only one degree of freedom.

 

[crucifige]

Thank you so much for replying.

So that, in order to apply Lagrangian dynamics,

Does it look right or am i missing something?

 

[TSny]

I think you're missing a type of kinetic energy.

 

[crucifige]

Should i add rotational motion into the kinetic energy? But cylinder is not moving, what do you think about the type of kinetic energy i am missing?

 

[vela]

Why do you think the cylinder isn't moving? The problem statement says it rolls without slipping.

 

[crucifige]

yes it is, but it is only moving at vertical axis, k₂ has told to be fixed on the vertical axis by the asker, it doesn't take any diagonal positions.

 

[vela]

So what happens when the wedge shifts horizontally?

 

[Kidphysics]

Had to ask the question about y= x(t) g a... is y= x(t) tangent(alpha)? and how do you derive that? thanks!