Write down the Lagrangian for a cylinder mass m, radius R an moment of inertia I, that rolls without slipping straight down an inclined plane which is at an angle a from the horizontal. Use as your generalized coordinate the cylinder's distance x measure down the plane from its starting point. Write down the Lagrange equation and solve it for the cylinder's acceleration.
The Attempt at a Solution
I tried to find the Lagrangian, this is what i have so far, is it right?
i said that T=1/2mv2+1/2Iw2
and U= -mgxsina so my Lagrangian would be
I think this is correct, but I'm not positive. If it is right then should i write I and w (omega) differently? and then continue with the partial differentiation?