Is My Lagrangian Setup for a Particle on an Inclined Plane Correct?

[Rob Hal]

Hi,

I'm looking for some advice on whether or not I'm doing a problem correctly.

The problem is:
A particle of mass m rests on a smooth plane. (the particle starts at r) The plane is raised to an inclination $$\theta$$, at a constant rate $$\alpha$$, with $$\theta = 0$$ at t=0, causing the particle to move down the plane.

So, I'm taking the x to be the distance the particle travels down the slope.

I come up with the following as the Lagrangian:

$$L = \frac{1}{2} m\dot{x}^2 - mg(r-x)sin\theta$$

I'm not sure if this is correct.

I would then get the equations of motion to be $$mgsin\theta - m\ddot{x}=0$$ and $$-mgsin(r-x)cos\theta=0$$.

 

[quantumdude]

Sorry for the late reply. In case you're still interested, here's my response to this question.

So, I'm taking the x to be the distance the particle travels down the slope.
I come up with the following as the Lagrangian:
$$L = \frac{1}{2} m\dot{x}^2 - mg(r-x)sin\theta$$

The KE term isn't right. It should have 2 terms, and one should contain an $\alpha$. The PE term is OK.