Write down the Hamiltonian for a solid cylinder $($mass $,$ radius $,$ and moment of inertial $=122)$ that rolls without slipping straight down an inclined plane which is at an angle from the horizontal. Use the cylinders distance measured down the plane from its starting point as your generalized coordinate. Write down the Hamiltons equation and solve it for the cylinders acceleration $.$ Remember that $=122+122,$ where is the velocity of the center of mass and is the angular velocity.